-lemma lpxs_ind (h) (G): ∀Q:relation lenv.
- Q (⋆) (⋆) → (
- ∀I,K1,K2.
- ⦃G, K1⦄ ⊢ ⬈*[h] K2 →
- Q K1 K2 → Q (K1.ⓘ{I}) (K2.ⓘ{I})
- ) → (
- ∀I,K1,K2,V1,V2.
- ⦃G, K1⦄ ⊢ ⬈*[h] K2 → ⦃G, K1⦄ ⊢ V1 ⬈*[h] V2 →
- Q K1 K2 → Q (K1.ⓑ{I}V1) (K2.ⓑ{I}V2)
- ) →
- ∀L1,L2. ⦃G, L1⦄ ⊢ ⬈*[h] L2 → Q L1 L2.
+lemma lpxs_ind (G) (Q:relation …):
+ Q (⋆) (⋆) → (
+ ∀I,K1,K2.
+ ❪G,K1❫ ⊢ ⬈* K2 →
+ Q K1 K2 → Q (K1.ⓘ[I]) (K2.ⓘ[I])
+ ) → (
+ ∀I,K1,K2,V1,V2.
+ ❪G,K1❫ ⊢ ⬈* K2 → ❪G,K1❫ ⊢ V1 ⬈* V2 →
+ Q K1 K2 → Q (K1.ⓑ[I]V1) (K2.ⓑ[I]V2)
+ ) →
+ ∀L1,L2. ❪G,L1❫ ⊢ ⬈* L2 → Q L1 L2.