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Start coqeq_complete

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Yiyun Liu 2025-02-13 17:46:35 -05:00
parent 0a70be3e57
commit 849169be7f
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16
theories/algorithmic.v
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@ -386,4 +386,18 @@ Proof.
Qed. Qed.
Definition algo_metric n (a b : PTm n) := Definition algo_metric n (a b : PTm n) :=
exists i j va vb, nsteps LoRed.R i a va /\ nsteps LoRed.R j a vb /\ size_PTm va + size_PTm vb + i + j = n. exists i j va vb, nsteps LoRed.R i a va /\ nsteps LoRed.R j a vb /\ nf va /\ nf vb /\ size_PTm va + size_PTm vb + i + j = n.
Lemma ishne_red n (a : PTm n) : SN a -> ~ ishne a -> exists b, HRed.R a b.
Admitted.
Lemma coqeq_complete n (a b : PTm n) :
algo_metric n a b -> DJoin.R a b ->
(forall Γ A, Γ ⊢ a ∈ A -> Γ ⊢ b ∈ A -> a ⇔ b) /\
(forall Γ A B, ishne a -> ishne b -> Γ ⊢ a ∈ A -> Γ ⊢ b ∈ B -> a ∼ b /\ exists C, Γ ⊢ C ≲ A /\ Γ ⊢ C ≲ B).
Proof.
move : n a b.
elim /Wf_nat.lt_wf_ind.
move => n ih.
move => a.
case /orP : (orNb (ishf a)).