Transfinite Constructions in Classical Type Theory

Global Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _ other (230 entries)
Notation Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _ other (6 entries)
Module Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _ other (2 entries)
Variable Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _ other (37 entries)
Library Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _ other (4 entries)
Lemma Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _ other (95 entries)
Constructor Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _ other (6 entries)
Inductive Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _ other (3 entries)
Projection Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _ other (14 entries)
Section Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _ other (14 entries)
Instance Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _ other (1 entry)
Abbreviation Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _ other (9 entries)
Definition Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _ other (36 entries)
Record Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _ other (3 entries)

Global Index

A

adj [definition, in SpecialTower]
adj_incl [lemma, in SpecialTower]
adj_fix [lemma, in SpecialTower]
anti_on [definition, in Preliminaries]


B

bot [definition, in CompletePartialOrder]
botP [lemma, in CompletePartialOrder]
BourbakiWitt [lemma, in GeneralTower]
BourbakiWitt [section, in GeneralTower]
BourbakiWittWo [lemma, in GeneralTower]
BourbakiWittWo [section, in GeneralTower]
BourbakiWittWo.f [variable, in GeneralTower]
BourbakiWittWo.f_ext [variable, in GeneralTower]
BourbakiWittWo.T [variable, in GeneralTower]
BourbakiWittWo.wo_Sup [variable, in GeneralTower]
BourbakiWitt.chain_Sup [variable, in GeneralTower]
BourbakiWitt.f [variable, in GeneralTower]
BourbakiWitt.f_ext [variable, in GeneralTower]
BourbakiWitt.T [variable, in GeneralTower]


C

chain [definition, in Preliminaries]
Chains [section, in Preliminaries]
ChainsP [lemma, in GeneralTower]
Chains.R [variable, in Preliminaries]
Chains.X [variable, in Preliminaries]
chainU [lemma, in Preliminaries]
chain_Sup_mono [lemma, in GeneralTower]
cmp [definition, in Preliminaries]
compare_adj [lemma, in SpecialTower]
compare_union [lemma, in SpecialTower]
complement [abbreviation, in Preliminaries]
CompletePartialOrder [record, in CompletePartialOrder]
CompletePartialOrder [library]
complete_fixed_point [lemma, in GeneralTower]
co_choice_eta [lemma, in GeneralTower]


E

ELE_linear [lemma, in Preliminaries]
ELE_on [definition, in Preliminaries]
eq_sub [lemma, in Preliminaries]
eta [definition, in GeneralTower]
etaN_full [lemma, in SpecialTower]
eta_inj [lemma, in SpecialTower]
eta_ssub_neq [lemma, in SpecialTower]
eta_fix [lemma, in SpecialTower]
eta_full_empty [lemma, in SpecialTower]
ExtChoiceFacts [section, in Preliminaries]
ExtChoiceFacts.X [variable, in Preliminaries]
ExtChoiceType [record, in Preliminaries]
ExtType [record, in Preliminaries]
ExtTypeFacts [section, in Preliminaries]
ExtTypeFacts.X [variable, in Preliminaries]
ext_sort [projection, in Preliminaries]


F

f [definition, in GeneralTower]
Facts [section, in CompletePartialOrder]
Facts.T [variable, in CompletePartialOrder]
fixed_point_greatest [lemma, in GeneralTower]
fixed_point_reach [lemma, in GeneralTower]
f_ext [lemma, in GeneralTower]


G

gamma [projection, in Preliminaries]
gammaP1 [projection, in Preliminaries]
gammaP2 [projection, in Preliminaries]
gamma_unique [lemma, in Preliminaries]
gamma0Vx [lemma, in Preliminaries]
GeneralHausdorff [lemma, in GeneralTower]
GeneralHausdorff [section, in GeneralTower]
GeneralHausdorff.c [variable, in GeneralTower]
GeneralHausdorff.chain_c [variable, in GeneralTower]
GeneralHausdorff.R [variable, in GeneralTower]
GeneralHausdorff.X [variable, in GeneralTower]
GeneralTower [section, in GeneralTower]
GeneralTower [library]
GeneralTower.c [variable, in GeneralTower]
GeneralTower.closed_mono [variable, in GeneralTower]
GeneralTower.f [variable, in GeneralTower]
GeneralTower.f_ext [variable, in GeneralTower]
GeneralTower.T [variable, in GeneralTower]
_ |> _ [notation, in GeneralTower]


H

Hausdorff [module, in SpecialTower]
Hausdorff.chain [definition, in SpecialTower]
Hausdorff.ChainsP [lemma, in SpecialTower]
Hausdorff.co_choice_eta [lemma, in SpecialTower]
Hausdorff.eta [definition, in SpecialTower]
Hausdorff.Hausdorff [lemma, in SpecialTower]
Hausdorff.Hausdorff [section, in SpecialTower]
Hausdorff.Hausdorff.R [variable, in SpecialTower]
Hausdorff.Hausdorff.X [variable, in SpecialTower]
Hausdorff.linear_Chains [lemma, in SpecialTower]
Hausdorff.Stage [abbreviation, in SpecialTower]
Hausdorff.unique_eta [lemma, in SpecialTower]


I

incl [definition, in Preliminaries]
inhab [definition, in Preliminaries]
inhab_gamma [lemma, in Preliminaries]
injective [definition, in Preliminaries]
Inter [definition, in Preliminaries]
inter_full [lemma, in Preliminaries]
inter_eq [lemma, in Preliminaries]
inter1 [lemma, in Preliminaries]
into [definition, in Preliminaries]


J

join [projection, in CompletePartialOrder]
join_eqI [lemma, in CompletePartialOrder]
join_mono [lemma, in CompletePartialOrder]
join_ub [lemma, in CompletePartialOrder]
join_le [lemma, in CompletePartialOrder]
join_Reach_fix [lemma, in GeneralTower]
join_Reach_greatest [lemma, in GeneralTower]


L

le [projection, in CompletePartialOrder]
least [definition, in Preliminaries]
le_join [lemma, in CompletePartialOrder]
le_joinP [projection, in CompletePartialOrder]
le_trans [projection, in CompletePartialOrder]
le_tsym [projection, in CompletePartialOrder]
le_refl [projection, in CompletePartialOrder]
le_Reach [lemma, in GeneralTower]
linearity [lemma, in SpecialTower]
linearity [lemma, in GeneralTower]
linears [definition, in Preliminaries]
linear_refl [lemma, in Preliminaries]
linear_on [definition, in Preliminaries]
linear_Chains [lemma, in GeneralTower]
lo_on [definition, in Preliminaries]
ltype [projection, in CompletePartialOrder]


O

OrderOn [section, in Preliminaries]
OrderOn.p [variable, in Preliminaries]
OrderOn.R [variable, in Preliminaries]
OrderOn.X [variable, in Preliminaries]


P

po_incl [lemma, in Preliminaries]
po_sub [lemma, in Preliminaries]
po_on [definition, in Preliminaries]
Predicates [section, in Preliminaries]
Predicates.X [variable, in Preliminaries]
Preliminaries [library]


R

Reach [inductive, in GeneralTower]
ReachJ [constructor, in GeneralTower]
Reach_wo [lemma, in GeneralTower]
Reach_ELE [lemma, in GeneralTower]
Reach_wf [lemma, in GeneralTower]
Reach_join [lemma, in GeneralTower]
Reach_sandwich [lemma, in GeneralTower]
Reach_linearity [lemma, in GeneralTower]
Reach_linearity_aux [lemma, in GeneralTower]
Reach_linearity_succ [lemma, in GeneralTower]
Reach_inv [lemma, in GeneralTower]
Reach_le [lemma, in GeneralTower]
Reach_trans [lemma, in GeneralTower]
Reach0 [constructor, in GeneralTower]
Reach1 [constructor, in GeneralTower]
refl_on [definition, in Preliminaries]
relation [abbreviation, in Preliminaries]


S

sandwich [lemma, in SpecialTower]
set [abbreviation, in Preliminaries]
setT [abbreviation, in Preliminaries]
setU0 [lemma, in Preliminaries]
setU1 [definition, in Preliminaries]
set_eqx [lemma, in Preliminaries]
set_ext [projection, in Preliminaries]
set_eq [lemma, in Preliminaries]
set0 [abbreviation, in Preliminaries]
set1 [abbreviation, in Preliminaries]
single [definition, in Preliminaries]
sort [projection, in Preliminaries]
SpecialTower [library]
Stage [inductive, in SpecialTower]
StgA [constructor, in SpecialTower]
StgT [lemma, in SpecialTower]
StgU [constructor, in SpecialTower]
StgU_full [lemma, in SpecialTower]
strong_join [lemma, in GeneralTower]
sub_union [lemma, in Preliminaries]
sub_trans [lemma, in Preliminaries]
sub_linear [lemma, in Preliminaries]
sub_refl [lemma, in Preliminaries]
Sup [projection, in CompletePartialOrder]


T

T [definition, in GeneralTower]
Tower [section, in SpecialTower]
tower_inter [lemma, in SpecialTower]
tower_wo [lemma, in SpecialTower]
tower_least [lemma, in SpecialTower]
Tower.eta [variable, in SpecialTower]
Tower.eta_greedy [variable, in SpecialTower]
Tower.eta_uniq [variable, in SpecialTower]
Tower.eta_ext [variable, in SpecialTower]
Tower.X [variable, in SpecialTower]
transfer_on [lemma, in Preliminaries]
Transitivity_le [instance, in CompletePartialOrder]
trans_on [definition, in Preliminaries]


U

Union [definition, in Preliminaries]
unionP [lemma, in GeneralTower]
unique [definition, in Preliminaries]
unique_eq1 [lemma, in Preliminaries]


W

wf [inductive, in GeneralTower]
wfI [constructor, in GeneralTower]
wf_inv [lemma, in GeneralTower]
wo_sub [lemma, in Preliminaries]
wo_on [definition, in Preliminaries]
wo_Sup_mono [lemma, in GeneralTower]


Z

Zermelo [module, in SpecialTower]
Zermelo.adj [abbreviation, in SpecialTower]
Zermelo.agrees [definition, in SpecialTower]
Zermelo.agrees_bar [lemma, in SpecialTower]
Zermelo.bar [definition, in SpecialTower]
Zermelo.barN [lemma, in SpecialTower]
Zermelo.barP [lemma, in SpecialTower]
Zermelo.bar_suj [lemma, in SpecialTower]
Zermelo.bar_seg [lemma, in SpecialTower]
Zermelo.bar_sub [lemma, in SpecialTower]
Zermelo.bar_rel [definition, in SpecialTower]
Zermelo.cochoice_eta [lemma, in SpecialTower]
Zermelo.eta [definition, in SpecialTower]
Zermelo.Extension [lemma, in SpecialTower]
Zermelo.Extension [section, in SpecialTower]
Zermelo.Extension.R [variable, in SpecialTower]
Zermelo.Extension.well_founded_R [variable, in SpecialTower]
Zermelo.Extension.X [variable, in SpecialTower]
Zermelo.gammaP1' [lemma, in SpecialTower]
Zermelo.gammaP2' [lemma, in SpecialTower]
Zermelo.gamma' [definition, in SpecialTower]
Zermelo.greedy_eta [lemma, in SpecialTower]
Zermelo.inj_bar [lemma, in SpecialTower]
Zermelo.min [definition, in SpecialTower]
Zermelo.Seg [definition, in SpecialTower]
Zermelo.Stage [abbreviation, in SpecialTower]
Zermelo.stage_bar [lemma, in SpecialTower]
Zermelo.unique_eta [lemma, in SpecialTower]
Zermelo.wo_bar_rel [lemma, in SpecialTower]
Zermelo.X' [definition, in SpecialTower]
Zermelo.Zermelo [lemma, in SpecialTower]
Zermelo.Zermelo [section, in SpecialTower]
Zermelo.Zermelo.X [variable, in SpecialTower]


other

_ <= _ (poset_scope) [notation, in CompletePartialOrder]
_ :|: _ [notation, in Preliminaries]
_ << _ [notation, in Preliminaries]
_ === _ [notation, in Preliminaries]
_ <<= _ [notation, in Preliminaries]



Notation Index

G

_ |> _ [in GeneralTower]


other

_ <= _ (poset_scope) [in CompletePartialOrder]
_ :|: _ [in Preliminaries]
_ << _ [in Preliminaries]
_ === _ [in Preliminaries]
_ <<= _ [in Preliminaries]



Module Index

H

Hausdorff [in SpecialTower]


Z

Zermelo [in SpecialTower]



Variable Index

B

BourbakiWittWo.f [in GeneralTower]
BourbakiWittWo.f_ext [in GeneralTower]
BourbakiWittWo.T [in GeneralTower]
BourbakiWittWo.wo_Sup [in GeneralTower]
BourbakiWitt.chain_Sup [in GeneralTower]
BourbakiWitt.f [in GeneralTower]
BourbakiWitt.f_ext [in GeneralTower]
BourbakiWitt.T [in GeneralTower]


C

Chains.R [in Preliminaries]
Chains.X [in Preliminaries]


E

ExtChoiceFacts.X [in Preliminaries]
ExtTypeFacts.X [in Preliminaries]


F

Facts.T [in CompletePartialOrder]


G

GeneralHausdorff.c [in GeneralTower]
GeneralHausdorff.chain_c [in GeneralTower]
GeneralHausdorff.R [in GeneralTower]
GeneralHausdorff.X [in GeneralTower]
GeneralTower.c [in GeneralTower]
GeneralTower.closed_mono [in GeneralTower]
GeneralTower.f [in GeneralTower]
GeneralTower.f_ext [in GeneralTower]
GeneralTower.T [in GeneralTower]


H

Hausdorff.Hausdorff.R [in SpecialTower]
Hausdorff.Hausdorff.X [in SpecialTower]


O

OrderOn.p [in Preliminaries]
OrderOn.R [in Preliminaries]
OrderOn.X [in Preliminaries]


P

Predicates.X [in Preliminaries]


T

Tower.eta [in SpecialTower]
Tower.eta_greedy [in SpecialTower]
Tower.eta_uniq [in SpecialTower]
Tower.eta_ext [in SpecialTower]
Tower.X [in SpecialTower]


Z

Zermelo.Extension.R [in SpecialTower]
Zermelo.Extension.well_founded_R [in SpecialTower]
Zermelo.Extension.X [in SpecialTower]
Zermelo.Zermelo.X [in SpecialTower]



Library Index

C

CompletePartialOrder


G

GeneralTower


P

Preliminaries


S

SpecialTower



Lemma Index

A

adj_incl [in SpecialTower]
adj_fix [in SpecialTower]


B

botP [in CompletePartialOrder]
BourbakiWitt [in GeneralTower]
BourbakiWittWo [in GeneralTower]


C

ChainsP [in GeneralTower]
chainU [in Preliminaries]
chain_Sup_mono [in GeneralTower]
compare_adj [in SpecialTower]
compare_union [in SpecialTower]
complete_fixed_point [in GeneralTower]
co_choice_eta [in GeneralTower]


E

ELE_linear [in Preliminaries]
eq_sub [in Preliminaries]
etaN_full [in SpecialTower]
eta_inj [in SpecialTower]
eta_ssub_neq [in SpecialTower]
eta_fix [in SpecialTower]
eta_full_empty [in SpecialTower]


F

fixed_point_greatest [in GeneralTower]
fixed_point_reach [in GeneralTower]
f_ext [in GeneralTower]


G

gamma_unique [in Preliminaries]
gamma0Vx [in Preliminaries]
GeneralHausdorff [in GeneralTower]


H

Hausdorff.ChainsP [in SpecialTower]
Hausdorff.co_choice_eta [in SpecialTower]
Hausdorff.Hausdorff [in SpecialTower]
Hausdorff.linear_Chains [in SpecialTower]
Hausdorff.unique_eta [in SpecialTower]


I

inhab_gamma [in Preliminaries]
inter_full [in Preliminaries]
inter_eq [in Preliminaries]
inter1 [in Preliminaries]


J

join_eqI [in CompletePartialOrder]
join_mono [in CompletePartialOrder]
join_ub [in CompletePartialOrder]
join_le [in CompletePartialOrder]
join_Reach_fix [in GeneralTower]
join_Reach_greatest [in GeneralTower]


L

le_join [in CompletePartialOrder]
le_Reach [in GeneralTower]
linearity [in SpecialTower]
linearity [in GeneralTower]
linear_refl [in Preliminaries]
linear_Chains [in GeneralTower]


P

po_incl [in Preliminaries]
po_sub [in Preliminaries]


R

Reach_wo [in GeneralTower]
Reach_ELE [in GeneralTower]
Reach_wf [in GeneralTower]
Reach_join [in GeneralTower]
Reach_sandwich [in GeneralTower]
Reach_linearity [in GeneralTower]
Reach_linearity_aux [in GeneralTower]
Reach_linearity_succ [in GeneralTower]
Reach_inv [in GeneralTower]
Reach_le [in GeneralTower]
Reach_trans [in GeneralTower]


S

sandwich [in SpecialTower]
setU0 [in Preliminaries]
set_eqx [in Preliminaries]
set_eq [in Preliminaries]
StgT [in SpecialTower]
StgU_full [in SpecialTower]
strong_join [in GeneralTower]
sub_union [in Preliminaries]
sub_trans [in Preliminaries]
sub_linear [in Preliminaries]
sub_refl [in Preliminaries]


T

tower_inter [in SpecialTower]
tower_wo [in SpecialTower]
tower_least [in SpecialTower]
transfer_on [in Preliminaries]


U

unionP [in GeneralTower]
unique_eq1 [in Preliminaries]


W

wf_inv [in GeneralTower]
wo_sub [in Preliminaries]
wo_Sup_mono [in GeneralTower]


Z

Zermelo.agrees_bar [in SpecialTower]
Zermelo.barN [in SpecialTower]
Zermelo.barP [in SpecialTower]
Zermelo.bar_suj [in SpecialTower]
Zermelo.bar_seg [in SpecialTower]
Zermelo.bar_sub [in SpecialTower]
Zermelo.cochoice_eta [in SpecialTower]
Zermelo.Extension [in SpecialTower]
Zermelo.gammaP1' [in SpecialTower]
Zermelo.gammaP2' [in SpecialTower]
Zermelo.greedy_eta [in SpecialTower]
Zermelo.inj_bar [in SpecialTower]
Zermelo.stage_bar [in SpecialTower]
Zermelo.unique_eta [in SpecialTower]
Zermelo.wo_bar_rel [in SpecialTower]
Zermelo.Zermelo [in SpecialTower]



Constructor Index

R

ReachJ [in GeneralTower]
Reach0 [in GeneralTower]
Reach1 [in GeneralTower]


S

StgA [in SpecialTower]
StgU [in SpecialTower]


W

wfI [in GeneralTower]



Inductive Index

R

Reach [in GeneralTower]


S

Stage [in SpecialTower]


W

wf [in GeneralTower]



Projection Index

E

ext_sort [in Preliminaries]


G

gamma [in Preliminaries]
gammaP1 [in Preliminaries]
gammaP2 [in Preliminaries]


J

join [in CompletePartialOrder]


L

le [in CompletePartialOrder]
le_joinP [in CompletePartialOrder]
le_trans [in CompletePartialOrder]
le_tsym [in CompletePartialOrder]
le_refl [in CompletePartialOrder]
ltype [in CompletePartialOrder]


S

set_ext [in Preliminaries]
sort [in Preliminaries]
Sup [in CompletePartialOrder]



Section Index

B

BourbakiWitt [in GeneralTower]
BourbakiWittWo [in GeneralTower]


C

Chains [in Preliminaries]


E

ExtChoiceFacts [in Preliminaries]
ExtTypeFacts [in Preliminaries]


F

Facts [in CompletePartialOrder]


G

GeneralHausdorff [in GeneralTower]
GeneralTower [in GeneralTower]


H

Hausdorff.Hausdorff [in SpecialTower]


O

OrderOn [in Preliminaries]


P

Predicates [in Preliminaries]


T

Tower [in SpecialTower]


Z

Zermelo.Extension [in SpecialTower]
Zermelo.Zermelo [in SpecialTower]



Instance Index

T

Transitivity_le [in CompletePartialOrder]



Abbreviation Index

C

complement [in Preliminaries]


H

Hausdorff.Stage [in SpecialTower]


R

relation [in Preliminaries]


S

set [in Preliminaries]
setT [in Preliminaries]
set0 [in Preliminaries]
set1 [in Preliminaries]


Z

Zermelo.adj [in SpecialTower]
Zermelo.Stage [in SpecialTower]



Definition Index

A

adj [in SpecialTower]
anti_on [in Preliminaries]


B

bot [in CompletePartialOrder]


C

chain [in Preliminaries]
cmp [in Preliminaries]


E

ELE_on [in Preliminaries]
eta [in GeneralTower]


F

f [in GeneralTower]


H

Hausdorff.chain [in SpecialTower]
Hausdorff.eta [in SpecialTower]


I

incl [in Preliminaries]
inhab [in Preliminaries]
injective [in Preliminaries]
Inter [in Preliminaries]
into [in Preliminaries]


L

least [in Preliminaries]
linears [in Preliminaries]
linear_on [in Preliminaries]
lo_on [in Preliminaries]


P

po_on [in Preliminaries]


R

refl_on [in Preliminaries]


S

setU1 [in Preliminaries]
single [in Preliminaries]


T

T [in GeneralTower]
trans_on [in Preliminaries]


U

Union [in Preliminaries]
unique [in Preliminaries]


W

wo_on [in Preliminaries]


Z

Zermelo.agrees [in SpecialTower]
Zermelo.bar [in SpecialTower]
Zermelo.bar_rel [in SpecialTower]
Zermelo.eta [in SpecialTower]
Zermelo.gamma' [in SpecialTower]
Zermelo.min [in SpecialTower]
Zermelo.Seg [in SpecialTower]
Zermelo.X' [in SpecialTower]



Record Index

C

CompletePartialOrder [in CompletePartialOrder]


E

ExtChoiceType [in Preliminaries]
ExtType [in Preliminaries]



Global Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _ other (230 entries)
Notation Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _ other (6 entries)
Module Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _ other (2 entries)
Variable Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _ other (37 entries)
Library Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _ other (4 entries)
Lemma Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _ other (95 entries)
Constructor Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _ other (6 entries)
Inductive Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _ other (3 entries)
Projection Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _ other (14 entries)
Section Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _ other (14 entries)
Instance Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _ other (1 entry)
Abbreviation Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _ other (9 entries)
Definition Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _ other (36 entries)
Record Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _ other (3 entries)

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