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Finish indzero and indsuc rules

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Yiyun Liu 2025-02-25 15:46:22 -05:00
parent 890f97365c
commit 4dd2cd7cd8
2 changed files with 50 additions and 1 deletions
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19
theories/typing.v
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@ -42,6 +42,25 @@ Inductive Wt : forall {n}, (fin n -> PTm n) -> PTm n -> PTm n -> Prop :=
⊢ Γ ->
Γ ⊢ PUniv i : PTm n ∈ PUniv (S i)
| T_Nat n Γ i :
⊢ Γ ->
Γ ⊢ PNat : PTm n ∈ PUniv i
| T_Zero n Γ :
⊢ Γ ->
Γ ⊢ PZero : PTm n ∈ PNat
| T_Suc n Γ (a : PTm n) :
Γ ⊢ a ∈ PNat ->
Γ ⊢ PSuc a ∈ PNat
| T_Ind s Γ P (a : PTm s) b c i :
funcomp (ren_PTm shift) (scons PNat Γ) ⊢ P ∈ PUniv i ->
Γ ⊢ a ∈ PNat ->
Γ ⊢ b ∈ subst_PTm (scons PZero VarPTm) P ->
funcomp (ren_PTm shift)(scons P (funcomp (ren_PTm shift) (scons PNat Γ))) ⊢ c ∈ ren_PTm shift (subst_PTm (scons (PSuc (VarPTm var_zero)) (funcomp VarPTm shift) ) P) ->
Γ ⊢ PInd P a b c ∈ subst_PTm (scons a VarPTm) P
| T_Conv n Γ (a : PTm n) A B :
Γ ⊢ a ∈ A ->
Γ ⊢ A ≲ B ->