yiyunliu/sp-eta-postpone
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity Actions

Finish the conversion proof completely

Browse source
This commit is contained in:
Yiyun Liu 2025-02-17 23:31:12 -05:00
parent 9c5eb31edf
commit d48d9db1b7
2 changed files with 91 additions and 25 deletions
Download patch file Download diff file Expand all files Collapse all files

29
theories/algorithmic.v
View file

@ -1617,3 +1617,32 @@ Proof.
hauto lq:on use:salgo_metric_algo_metric.
eapply coqeq_complete'; eauto.
Qed.
Lemma coqleq_complete n Γ (a b : PTm n) :
Γ ⊢ a ≲ b -> a ≪ b.
Proof.
move => h.
suff : exists k, salgo_metric k a b by hauto lq:on use:coqleq_complete', regularity.
eapply fundamental_theorem in h.
move /logrel.SemLEq_SN_Sub : h.
move => h.
have : exists va vb : PTm n,
rtc LoRed.R a va /\
rtc LoRed.R b vb /\ nf va /\ nf vb /\ ESub.R va vb
by hauto l:on use:Sub.standardization_lo.
move => [va][vb][hva][hvb][nva][nvb]hj.
move /relations.rtc_nsteps : hva => [i hva].
move /relations.rtc_nsteps : hvb => [j hvb].
exists (i + j + size_PTm va + size_PTm vb).
hauto lq:on solve+:lia.
Qed.
Lemma coqleq_sound : forall n Γ (a b : PTm n) i j,
Γ ⊢ a ∈ PUniv i -> Γ ⊢ b ∈ PUniv j -> a ≪ b -> Γ ⊢ a ≲ b.
Proof.
move => n Γ a b i j.
have [*] : i <= i + j /\ j <= i + j by lia.
have : Γ ⊢ a ∈ PUniv (i + j) /\ Γ ⊢ b ∈ PUniv (i + j)
by sfirstorder use:T_Univ_Raise.
sfirstorder use:coqleq_sound_mutual.
Qed.