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Renumber the lemmas
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Yiyun Liu 2025-07-10 18:25:54 -04:00
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@ -47,56 +47,55 @@ file from =syntax.sig= using =autosubst=, you can choose not to install =coq-aut
However, you need to be careful not to accidentally run =make clean=, However, you need to be careful not to accidentally run =make clean=,
which will delete the auto-generated syntax files. which will delete the auto-generated syntax files.
** Properties proven in the paper ** Properties proven in the paper
The definition of the logical relation is split into =InterpExt= and
=InterpUniv= in [[file:theories/logrel.v][logrel.v]].
*** Section 2 *** Section 2
- Lemma 2.1 (context regularity) :: [[file:./theories/structural.v][structural.v]], =wff_mutual= - Lemma 2.1 (context regularity) :: [[file:./theories/structural.v][structural.v]], =wff_mutual=
- Lemma 2.2 (generation) :: [[file:./theories/structural.v][structural.v]], [[file:theories/admissible.v][admissible.v]], =*_Inv= - Lemma 2.2 (generation) :: [[file:./theories/structural.v][structural.v]], [[file:theories/admissible.v][admissible.v]], =*_Inv=
- Lemma 2.3 (weakening) :: [[file:./theories/structural.v][structural.v]], =renaming= - Lemma 2.3 (subject reduction) :: [[file:theories/preservation.v][preservation.v]], =RRed_Eq=, =subject_reduction=
- Lemma 2.4 (substitution) :: [[file:./theories/structural.v][structural.v]], =substitution= - Lemma 2.4 (regularity) :: [[file:./theories/structural.v][structural.v]], =regularity=
- Lemma 2.5 (subject reduction) :: [[file:theories/preservation.v][preservation.v]], =RRed_Eq=, =subject_reduction=
- Lemma 2.6 (regularity) :: [[file:./theories/structural.v][structural.v]], =regularity=
*** Section 3 *** Section 3
- Lemma 3.1 :: [[file:theories/fp_red.v][fp_red.v]], =RRed.nf_imp= - Lemma 3.1 :: [[file:theories/fp_red.v][fp_red.v]], =RRed.nf_imp=
- Lemma 3.3 :: [[file:theories/fp_red.v][fp_red.v]], =ERed.nf_preservation= - Lemma 3.2 :: [[file:theories/fp_red.v][fp_red.v]], =ERed.nf_preservation=
- Lemma 3.4 :: [[file:theories/fp_red.v][fp_red.v]], =LoReds.FromSN_mutual= - Lemma 3.3 :: [[file:theories/fp_red.v][fp_red.v]], =LoReds.FromSN_mutual=
- Lemma 3.5 (no stuck terms) :: [[file:theories/fp_red.v][fp_red.v]], =SN_NoForbid.*_imp= - Lemma 3.4 (no stuck terms) :: [[file:theories/fp_red.v][fp_red.v]], =SN_NoForbid.*_imp=
- Lemma 3.6 (sn renaming) :: [[file:theories/fp_red.v][fp_red.v]], =sn_renaming= - Lemma 3.5 (sn antisubstitution) :: [[file:theories/fp_red.v][fp_red.v]], =sn_unmorphing=
- Lemma 3.7 (sn antisubstitution) :: [[file:theories/fp_red.v][fp_red.v]], =sn_unmorphing= - Lemma 3.6 (sn preservation) :: [[file:theories/fp_red.v][fp_red.v]], =RERed.sn_preservation=,
- Lemma 3.8 (sn inversion) :: [[file:theories/fp_red.v][fp_red.v]], =SN_NoForbid.P_*Inv=
- Lemma 3.9 (sn preservation) :: [[file:theories/fp_red.v][fp_red.v]], =RERed.sn_preservation=,
=epar_sn_preservation=, =red_sn_preservation= =epar_sn_preservation=, =red_sn_preservation=
- Lemma 3.10 (nonelim and elim) :: [[file:theories/fp_red.v][fp_red.v]], =R_nonelim_nothf=, =R_elim_nonelim= - Lemma 3.7 (restrictive-$\eta$ and normal form) :: [[file:theories/fp_red.v][fp_red.v]], =R_elim_nf=
- Lemma 3.11 (restrictive-$\eta$ and normal form) :: [[file:theories/fp_red.v][fp_red.v]], =R_elim_nf= - Lemma 3.8 ($\eta$-decomposition) :: [[file:theories/fp_red.v][fp_red.v]], =η_split=
- Lemma 3.12 ($\eta$-decomposition) :: [[file:theories/fp_red.v][fp_red.v]], =η_split= - Lemma 3.9 ($\eta$-postponement) :: [[file:theories/fp_red.v][fp_red.v]], =eta_postponement=
- Lemma 3.13 ($\eta$-postponement) :: [[file:theories/fp_red.v][fp_red.v]], =eta_postponement=
- Corollary 3.1 (strengthened $\eta$-postponement) :: [[file:theories/fp_red.v][fp_red.v]], =eta_postponement_star'= - Corollary 3.1 (strengthened $\eta$-postponement) :: [[file:theories/fp_red.v][fp_red.v]], =eta_postponement_star'=
- Corollary 3.2 ($\eta$-postponement for normal forms) :: [[file:theories/fp_red.v][fp_red.v]], =standardization= - Corollary 3.2 ($\eta$-postponement for normal forms) :: [[file:theories/fp_red.v][fp_red.v]], =standardization=
- Lemma 3.14 (confluence for $\beta$) :: [[file:theories/fp_red.v][fp_red.v]], =red_confluence= - Lemma 3.10 (confluence for $\beta$) :: [[file:theories/fp_red.v][fp_red.v]], =red_confluence=
- Lemma 3.15 (confluence for $\eta$) :: [[file:theories/fp_red.v][fp_red.v]], =ered_confluence= - Lemma 3.11 (confluence for $\eta$) :: [[file:theories/fp_red.v][fp_red.v]], =ered_confluence=
- Theorem 3.1 (confluence for $\beta\eta$ :: [[file:theories/fp_red.v][fp_red.v]], =rered_confluence= - Theorem 3.1 (confluence for $\beta\eta$ :: [[file:theories/fp_red.v][fp_red.v]], =rered_confluence=
- Lemma 3.16 (transitivity of joinability) :: [[file:theories/fp_red.v][fp_red.v]], =DJoin.transitive= - Lemma 3.12 (transitivity of joinability) :: [[file:theories/fp_red.v][fp_red.v]], =DJoin.transitive=
- Lemma 3.17 (injectivity of joinability) :: [[file:theories/fp_red.v][fp_red.v]], - Lemma 3.13 (injectivity of joinability) :: [[file:theories/fp_red.v][fp_red.v]],
=DJoin.hne_app_inj=, =DJoin.hne_proj_inj= =DJoin.hne_app_inj=, =DJoin.hne_proj_inj=
- Lemma 3.18 (transitivity of one-step subtyping) :: [[file:theories/fp_red.v][fp_red.v]], - Lemma 3.14 (transitivity of one-step subtyping) :: [[file:theories/fp_red.v][fp_red.v]],
=Sub1.transitive= =Sub1.transitive=
- Lemma 3.19 (commutativity of one-step subtyping) :: [[file:theories/fp_red.v][fp_red.v]], =Sub1.commutativity0= - Lemma 3.15 (commutativity of one-step subtyping) :: [[file:theories/fp_red.v][fp_red.v]], =Sub1.commutativity0=
- Lemma 3.20 (one-step subtyping preserves sn) :: [[file:theories/fp_red.v][fp_red.v]], =Sub1.sn_preservation= - Lemma 3.16 (one-step subtyping preserves sn) :: [[file:theories/fp_red.v][fp_red.v]], =Sub1.sn_preservation=
- Corollary 3.3 (transitivity of untyped subtyping) :: [[file:theories/fp_red.v][fp_red.v]], =Sub.transitive= - Corollary 3.3 (transitivity of untyped subtyping) :: [[file:theories/fp_red.v][fp_red.v]], =Sub.transitive=
- Lemma 3.21 (noconfusion for untyped subtyping) :: [[file:theories/fp_red.v][fp_red.v]], =Sub.*_noconf= - Lemma 3.17 (noconfusion for untyped subtyping) :: [[file:theories/fp_red.v][fp_red.v]], =Sub.*_noconf=
- Lemma 3.22 (untyped injectivity of type constructors) :: [[file:theories/fp_red.v][fp_red.v]], =Sub.*_inj= - Lemma 3.18 (untyped injectivity of type constructors) :: [[file:theories/fp_red.v][fp_red.v]], =Sub.*_inj=
- Lemma 3.23 (adequacy) :: [[file:theories/logrel.v][logrel.v]], =adequacy= - Lemma 3.19 (adequacy) :: [[file:theories/logrel.v][logrel.v]], =adequacy=
- Lemma 3.24 (backward closure) :: [[file:theories/logrel.v][logrel.v]], =InterpUniv_back_clos= - Lemma 3.20 (backward closure) :: [[file:theories/logrel.v][logrel.v]], =InterpUniv_back_clos=
- Lemma 3.25 (logical predicate cases) :: [[file:theories/logrel.v][logrel.v]], =InterpUniv_case= - Lemma 3.21 (logical predicate cases) :: [[file:theories/logrel.v][logrel.v]], =InterpUniv_case=
- Lemma 3.26 (logical predicate is preserved by subtyping) :: - Lemma 3.22 (logical predicate is preserved by subtyping) ::
[[file:theories/logrel.v][logrel.v]], =InterpUniv_Sub0= [[file:theories/logrel.v][logrel.v]], =InterpUniv_Sub0=
- Lemma 3.4 (logical predicate is preserved by subtyping) :: [[file:theories/logrel.v][logrel.v]], =InterpUniv_Sub0=
- Corollary 3.4 (logical predicate is functional) :: [[file:theories/logrel.v][logrel.v]], =InterpUniv_Functional= - Corollary 3.4 (logical predicate is functional) :: [[file:theories/logrel.v][logrel.v]], =InterpUniv_Functional=
- Lemma 3.27 (logical predicate is cumulative) :: [[file:theories/logrel.v][logrel.v]], =InterpUniv_cumulative= - Lemma 3.23 (logical predicate is cumulative) :: [[file:theories/logrel.v][logrel.v]], =InterpUniv_cumulative=
- Lemma 3.28 (semantic weakening) :: [[file:theories/logrel.v][logrel.v]], =weakening_Sem= - Lemma 3.24 (semantic weakening) :: [[file:theories/logrel.v][logrel.v]], =weakening_Sem=
- Lemma 3.29 (semantic substitution) :: [[file:theories/logrel.v][logrel.v]], =morphing_SemWt= - Lemma 3.25 (semantic substitution) :: [[file:theories/logrel.v][logrel.v]], =morphing_SemWt=
- Lemma 3.30 (structural rules for semantic well-formedness) :: [[file:theories/logrel.v][logrel.v]], =SemWff= - Lemma 3.26 (structural rules for semantic well-formedness) :: [[file:theories/logrel.v][logrel.v]], =SemWff=
- Theorem 3.2 (fundamental theorem) :: [[file:theories/soundness.v][soundness.v]], =fundamental_theorem= - Theorem 3.2 (fundamental theorem) :: [[file:theories/soundness.v][soundness.v]], =fundamental_theorem=
- Corollary 3.5 (completeness of reduce-and-compare) :: Inlined into
proof scripts
- Corollary 3.6 (completeness of reduce-and-compare) :: [[file:theories/soundness.v][soundness.v]], =synsub_to_usub= - Corollary 3.6 (completeness of reduce-and-compare) :: [[file:theories/soundness.v][soundness.v]], =synsub_to_usub=
*** Section 4 *** Section 4
- Lemma 4.1 ($\Pi$-subtyping) :: [[file:theories/logrel.v][logrel.v]], =Sub_Bind_Inv{L,R}= - Lemma 4.1 ($\Pi$-subtyping) :: [[file:theories/logrel.v][logrel.v]], =Sub_Bind_Inv{L,R}=
@ -106,6 +105,10 @@ which will delete the auto-generated syntax files.
- Lemma 4.5 (metric implies domain) :: [[file:theories/algorithmic.v][algorithmic.v]], =sn_term_metric= - Lemma 4.5 (metric implies domain) :: [[file:theories/algorithmic.v][algorithmic.v]], =sn_term_metric=
- Lemma 4.6 (termination of Coquand's algorithm) :: [[file:theories/executable.v][executable.v]], =check_sub= - Lemma 4.6 (termination of Coquand's algorithm) :: [[file:theories/executable.v][executable.v]], =check_sub=
- Lemma 4.7 (completeness of Coquand's algorithm) :: [[file:theories/algorithmic.v][algorithmic.v]], =coqeq_complete'= - Lemma 4.7 (completeness of Coquand's algorithm) :: [[file:theories/algorithmic.v][algorithmic.v]], =coqeq_complete'=
- Lemma 4.8 (completeness of Coquand's algorithmic subtyping) :: [[file:theories/algorithmic.v][algorithmic.v]], =coqleq_complete'= - Lemma 4.8 (completeness of Coquand's algorithmic subtyping) ::
[[file:theories/algorithmic.v][algorithmic.v]], =coqleq_complete'=
- Lemma 4.9 (completeness of Coquand's algorithmic subtyping) ::
[[file:theories/algorithmic.v][algorithmic.v]], lemmas near the end of the file
- Theorem 4.1 :: by composing 4.9 and 4.6
*** Section 5 *** Section 5
- Proposition 5.1 :: [[file:theories/cosn.v][cosn.v]] =Safe_NoForbid= - Proposition 5.1 :: [[file:theories/cosn.v][cosn.v]] =Safe_NoForbid=