Theorem: Lean4Lean.VEnv.IsDefEq.weakN (Lean4Lean/Theory/Typing/Lemmas.lean)

State before:
env : VEnv
henv : Ordered env
n k : Nat
Γ Γ' : List VExpr
U : Nat
e1 e2 A : VExpr
W : Ctx.LiftN n k Γ Γ'
H : IsDefEq env U Γ e1 e2 A
⊢ IsDefEq env U Γ' (liftN n e1 k) (liftN n e2 k) (liftN n A k)
Tactic:
induction H generalizing k Γ' with
| bvar h => refine .bvar (h.weakN W)
| symm _ ih => exact .symm (ih W)
| trans _ _ ih1 ih2 => exact .trans (ih1 W) (ih2 W)
| sortDF h1 h2 h3 => exact .sortDF h1 h2 h3
| constDF h1 h2 h3 h4 h5 =>
  rw [(henv.closedC h1).instL.liftN_eq (Nat.zero_le _)]
  exact .constDF h1 h2 h3 h4 h5
| appDF _ _ ih1 ih2 => exact liftN_inst_hi .. ▸ .appDF (ih1 W) (ih2 W)
| lamDF _ _ ih1 ih2 => exact .lamDF (ih1 W) (ih2 W.succ)
| forallEDF _ _ ih1 ih2 => exact .forallEDF (ih1 W) (ih2 W.succ)
| defeqDF _ _ ih1 ih2 => exact .defeqDF (ih1 W) (ih2 W)
| beta _ _ ih1 ih2 =>
  exact VExpr.liftN_inst_hi .. ▸ VExpr.liftN_instN_hi .. ▸ .beta (ih1 W.succ) (ih2 W)
| eta _ ih =>
  have := IsDefEq.eta (ih W)
  simp [liftN]; rwa [← lift_liftN']
| proofIrrel _ _ _ ih1 ih2 ih3 => exact .proofIrrel (ih1 W) (ih2 W) (ih3 W)
| extra h1 h2 h3 =>
  have ⟨⟨hA1, _⟩, hA2, hA3⟩ := henv.closed.2 h1
  rw [
    hA1.instL.liftN_eq (Nat.zero_le _),
    hA2.instL.liftN_eq (Nat.zero_le _),
    hA3.instL.liftN_eq (Nat.zero_le _)]
  exact .extra h1 h2 h3
State after:
no goals

State before:
case bvar
env : VEnv
henv : Ordered env
n : Nat
Γ : List VExpr
U : Nat
e1 e2 A : VExpr
Γ✝ : List VExpr
i✝ : Nat
A✝ : VExpr
h : Lookup Γ✝ i✝ A✝
k : Nat
Γ' : List VExpr
W : Ctx.LiftN n k Γ✝ Γ'
⊢ IsDefEq env U Γ' (liftN n (VExpr.bvar i✝) k) (liftN n (VExpr.bvar i✝) k) (liftN n A✝ k)
Tactic:
refine .bvar (h.weakN W)
State after:
no goals

State before:
case symm
env : VEnv
henv : Ordered env
n : Nat
Γ : List VExpr
U : Nat
e1 e2 A : VExpr
Γ✝ : List VExpr
e✝ e'✝ A✝ : VExpr
a✝ : IsDefEq env U Γ✝ e✝ e'✝ A✝
ih : ∀ {k : Nat} {Γ' : List VExpr}, Ctx.LiftN n k Γ✝ Γ' → IsDefEq env U Γ' (liftN n e✝ k) (liftN n e'✝ k) (liftN n A✝ k)
k : Nat
Γ' : List VExpr
W : Ctx.LiftN n k Γ✝ Γ'
⊢ IsDefEq env U Γ' (liftN n e'✝ k) (liftN n e✝ k) (liftN n A✝ k)
Tactic:
exact .symm (ih W)
State after:
no goals

State before:
case trans
env : VEnv
henv : Ordered env
n : Nat
Γ : List VExpr
U : Nat
e1 e2 A : VExpr
Γ✝ : List VExpr
e₁✝ e₂✝ A✝ e₃✝ : VExpr
a✝¹ : IsDefEq env U Γ✝ e₁✝ e₂✝ A✝
a✝ : IsDefEq env U Γ✝ e₂✝ e₃✝ A✝
ih1 :
  ∀ {k : Nat} {Γ' : List VExpr}, Ctx.LiftN n k Γ✝ Γ' → IsDefEq env U Γ' (liftN n e₁✝ k) (liftN n e₂✝ k) (liftN n A✝ k)
ih2 :
  ∀ {k : Nat} {Γ' : List VExpr}, Ctx.LiftN n k Γ✝ Γ' → IsDefEq env U Γ' (liftN n e₂✝ k) (liftN n e₃✝ k) (liftN n A✝ k)
k : Nat
Γ' : List VExpr
W : Ctx.LiftN n k Γ✝ Γ'
⊢ IsDefEq env U Γ' (liftN n e₁✝ k) (liftN n e₃✝ k) (liftN n A✝ k)
Tactic:
exact .trans (ih1 W) (ih2 W)
State after:
no goals

State before:
case sortDF
env : VEnv
henv : Ordered env
n : Nat
Γ : List VExpr
U : Nat
e1 e2 A : VExpr
l✝ l'✝ : VLevel
Γ✝ : List VExpr
h1 : VLevel.WF U l✝
h2 : VLevel.WF U l'✝
h3 : l✝ ≈ l'✝
k : Nat
Γ' : List VExpr
W : Ctx.LiftN n k Γ✝ Γ'
⊢ IsDefEq env U Γ' (liftN n (VExpr.sort l✝) k) (liftN n (VExpr.sort l'✝) k) (liftN n (VExpr.sort (VLevel.succ l✝)) k)
Tactic:
exact .sortDF h1 h2 h3
State after:
no goals

State before:
case constDF
env : VEnv
henv : Ordered env
n : Nat
Γ : List VExpr
U : Nat
e1 e2 A : VExpr
c✝ : Name
ci✝ : VConstant
ls✝ ls'✝ : List VLevel
Γ✝ : List VExpr
h1 : env.constants c✝ = some (some ci✝)
h2 : ∀ (l : VLevel), l ∈ ls✝ → VLevel.WF U l
h3 : ∀ (l : VLevel), l ∈ ls'✝ → VLevel.WF U l
h4 : List.length ls✝ = ci✝.uvars
h5 : List.Forall₂ (fun x x_1 => x ≈ x_1) ls✝ ls'✝
k : Nat
Γ' : List VExpr
W : Ctx.LiftN n k Γ✝ Γ'
⊢ IsDefEq env U Γ' (liftN n (VExpr.const c✝ ls✝) k) (liftN n (VExpr.const c✝ ls'✝) k) (liftN n (instL ls✝ ci✝.type) k)
Tactic:
rw [(henv.closedC h1).instL.liftN_eq (Nat.zero_le _)]
State after:
case constDF
env : VEnv
henv : Ordered env
n : Nat
Γ : List VExpr
U : Nat
e1 e2 A : VExpr
c✝ : Name
ci✝ : VConstant
ls✝ ls'✝ : List VLevel
Γ✝ : List VExpr
h1 : env.constants c✝ = some (some ci✝)
h2 : ∀ (l : VLevel), l ∈ ls✝ → VLevel.WF U l
h3 : ∀ (l : VLevel), l ∈ ls'✝ → VLevel.WF U l
h4 : List.length ls✝ = ci✝.uvars
h5 : List.Forall₂ (fun x x_1 => x ≈ x_1) ls✝ ls'✝
k : Nat
Γ' : List VExpr
W : Ctx.LiftN n k Γ✝ Γ'
⊢ IsDefEq env U Γ' (liftN n (VExpr.const c✝ ls✝) k) (liftN n (VExpr.const c✝ ls'✝) k) (instL ls✝ ci✝.type)

State before:
case constDF
env : VEnv
henv : Ordered env
n : Nat
Γ : List VExpr
U : Nat
e1 e2 A : VExpr
c✝ : Name
ci✝ : VConstant
ls✝ ls'✝ : List VLevel
Γ✝ : List VExpr
h1 : env.constants c✝ = some (some ci✝)
h2 : ∀ (l : VLevel), l ∈ ls✝ → VLevel.WF U l
h3 : ∀ (l : VLevel), l ∈ ls'✝ → VLevel.WF U l
h4 : List.length ls✝ = ci✝.uvars
h5 : List.Forall₂ (fun x x_1 => x ≈ x_1) ls✝ ls'✝
k : Nat
Γ' : List VExpr
W : Ctx.LiftN n k Γ✝ Γ'
⊢ IsDefEq env U Γ' (liftN n (VExpr.const c✝ ls✝) k) (liftN n (VExpr.const c✝ ls'✝) k) (instL ls✝ ci✝.type)
Tactic:
exact .constDF h1 h2 h3 h4 h5
State after:
no goals

State before:
case appDF
env : VEnv
henv : Ordered env
n : Nat
Γ : List VExpr
U : Nat
e1 e2 A : VExpr
Γ✝ : List VExpr
f✝ f'✝ A✝ B✝ a✝² a'✝ : VExpr
a✝¹ : IsDefEq env U Γ✝ f✝ f'✝ (VExpr.forallE A✝ B✝)
a✝ : IsDefEq env U Γ✝ a✝² a'✝ A✝
ih1 :
  ∀ {k : Nat} {Γ' : List VExpr},
    Ctx.LiftN n k Γ✝ Γ' → IsDefEq env U Γ' (liftN n f✝ k) (liftN n f'✝ k) (liftN n (VExpr.forallE A✝ B✝) k)
ih2 :
  ∀ {k : Nat} {Γ' : List VExpr}, Ctx.LiftN n k Γ✝ Γ' → IsDefEq env U Γ' (liftN n a✝² k) (liftN n a'✝ k) (liftN n A✝ k)
k : Nat
Γ' : List VExpr
W : Ctx.LiftN n k Γ✝ Γ'
⊢ IsDefEq env U Γ' (liftN n (app f✝ a✝²) k) (liftN n (app f'✝ a'✝) k) (liftN n (inst B✝ a✝²) k)
Tactic:
exact liftN_inst_hi .. ▸ .appDF (ih1 W) (ih2 W)
State after:
no goals

State before:
case lamDF
env : VEnv
henv : Ordered env
n : Nat
Γ : List VExpr
U : Nat
e1 e2 A : VExpr
Γ✝ : List VExpr
A✝ A'✝ : VExpr
u✝ : VLevel
body✝ body'✝ B✝ : VExpr
a✝¹ : IsDefEq env U Γ✝ A✝ A'✝ (VExpr.sort u✝)
a✝ : IsDefEq env U (A✝ :: Γ✝) body✝ body'✝ B✝
ih1 :
  ∀ {k : Nat} {Γ' : List VExpr},
    Ctx.LiftN n k Γ✝ Γ' → IsDefEq env U Γ' (liftN n A✝ k) (liftN n A'✝ k) (liftN n (VExpr.sort u✝) k)
ih2 :
  ∀ {k : Nat} {Γ' : List VExpr},
    Ctx.LiftN n k (A✝ :: Γ✝) Γ' → IsDefEq env U Γ' (liftN n body✝ k) (liftN n body'✝ k) (liftN n B✝ k)
k : Nat
Γ' : List VExpr
W : Ctx.LiftN n k Γ✝ Γ'
⊢ IsDefEq env U Γ' (liftN n (lam A✝ body✝) k) (liftN n (lam A'✝ body'✝) k) (liftN n (VExpr.forallE A✝ B✝) k)
Tactic:
exact .lamDF (ih1 W) (ih2 W.succ)
State after:
no goals

State before:
case forallEDF
env : VEnv
henv : Ordered env
n : Nat
Γ : List VExpr
U : Nat
e1 e2 A : VExpr
Γ✝ : List VExpr
A✝ A'✝ : VExpr
u✝ : VLevel
body✝ body'✝ : VExpr
v✝ : VLevel
a✝¹ : IsDefEq env U Γ✝ A✝ A'✝ (VExpr.sort u✝)
a✝ : IsDefEq env U (A✝ :: Γ✝) body✝ body'✝ (VExpr.sort v✝)
ih1 :
  ∀ {k : Nat} {Γ' : List VExpr},
    Ctx.LiftN n k Γ✝ Γ' → IsDefEq env U Γ' (liftN n A✝ k) (liftN n A'✝ k) (liftN n (VExpr.sort u✝) k)
ih2 :
  ∀ {k : Nat} {Γ' : List VExpr},
    Ctx.LiftN n k (A✝ :: Γ✝) Γ' → IsDefEq env U Γ' (liftN n body✝ k) (liftN n body'✝ k) (liftN n (VExpr.sort v✝) k)
k : Nat
Γ' : List VExpr
W : Ctx.LiftN n k Γ✝ Γ'
⊢ IsDefEq env U Γ' (liftN n (VExpr.forallE A✝ body✝) k) (liftN n (VExpr.forallE A'✝ body'✝) k)
    (liftN n (VExpr.sort (VLevel.imax u✝ v✝)) k)
Tactic:
exact .forallEDF (ih1 W) (ih2 W.succ)
State after:
no goals

State before:
case defeqDF
env : VEnv
henv : Ordered env
n : Nat
Γ : List VExpr
U : Nat
e1 e2 A : VExpr
Γ✝ : List VExpr
A✝ B✝ : VExpr
u✝ : VLevel
e1✝ e2✝ : VExpr
a✝¹ : IsDefEq env U Γ✝ A✝ B✝ (VExpr.sort u✝)
a✝ : IsDefEq env U Γ✝ e1✝ e2✝ A✝
ih1 :
  ∀ {k : Nat} {Γ' : List VExpr},
    Ctx.LiftN n k Γ✝ Γ' → IsDefEq env U Γ' (liftN n A✝ k) (liftN n B✝ k) (liftN n (VExpr.sort u✝) k)
ih2 :
  ∀ {k : Nat} {Γ' : List VExpr}, Ctx.LiftN n k Γ✝ Γ' → IsDefEq env U Γ' (liftN n e1✝ k) (liftN n e2✝ k) (liftN n A✝ k)
k : Nat
Γ' : List VExpr
W : Ctx.LiftN n k Γ✝ Γ'
⊢ IsDefEq env U Γ' (liftN n e1✝ k) (liftN n e2✝ k) (liftN n B✝ k)
Tactic:
exact .defeqDF (ih1 W) (ih2 W)
State after:
no goals

State before:
case beta
env : VEnv
henv : Ordered env
n : Nat
Γ : List VExpr
U : Nat
e1 e2 A A✝ : VExpr
Γ✝ : List VExpr
e✝ B✝ e'✝ : VExpr
a✝¹ : IsDefEq env U (A✝ :: Γ✝) e✝ e✝ B✝
a✝ : IsDefEq env U Γ✝ e'✝ e'✝ A✝
ih1 :
  ∀ {k : Nat} {Γ' : List VExpr},
    Ctx.LiftN n k (A✝ :: Γ✝) Γ' → IsDefEq env U Γ' (liftN n e✝ k) (liftN n e✝ k) (liftN n B✝ k)
ih2 :
  ∀ {k : Nat} {Γ' : List VExpr}, Ctx.LiftN n k Γ✝ Γ' → IsDefEq env U Γ' (liftN n e'✝ k) (liftN n e'✝ k) (liftN n A✝ k)
k : Nat
Γ' : List VExpr
W : Ctx.LiftN n k Γ✝ Γ'
⊢ IsDefEq env U Γ' (liftN n (app (lam A✝ e✝) e'✝) k) (liftN n (inst e✝ e'✝) k) (liftN n (inst B✝ e'✝) k)
Tactic:
exact VExpr.liftN_inst_hi .. ▸ VExpr.liftN_instN_hi .. ▸ .beta (ih1 W.succ) (ih2 W)
State after:
no goals

State before:
case eta
env : VEnv
henv : Ordered env
n : Nat
Γ : List VExpr
U : Nat
e1 e2 A : VExpr
Γ✝ : List VExpr
e✝ A✝ B✝ : VExpr
a✝ : IsDefEq env U Γ✝ e✝ e✝ (VExpr.forallE A✝ B✝)
ih :
  ∀ {k : Nat} {Γ' : List VExpr},
    Ctx.LiftN n k Γ✝ Γ' → IsDefEq env U Γ' (liftN n e✝ k) (liftN n e✝ k) (liftN n (VExpr.forallE A✝ B✝) k)
k : Nat
Γ' : List VExpr
W : Ctx.LiftN n k Γ✝ Γ'
⊢ IsDefEq env U Γ' (liftN n (lam A✝ (app (lift e✝) (VExpr.bvar 0))) k) (liftN n e✝ k) (liftN n (VExpr.forallE A✝ B✝) k)
Tactic:
have := IsDefEq.eta (ih W)
State after:
case eta
env : VEnv
henv : Ordered env
n : Nat
Γ : List VExpr
U : Nat
e1 e2 A : VExpr
Γ✝ : List VExpr
e✝ A✝ B✝ : VExpr
a✝ : IsDefEq env U Γ✝ e✝ e✝ (VExpr.forallE A✝ B✝)
ih :
  ∀ {k : Nat} {Γ' : List VExpr},
    Ctx.LiftN n k Γ✝ Γ' → IsDefEq env U Γ' (liftN n e✝ k) (liftN n e✝ k) (liftN n (VExpr.forallE A✝ B✝) k)
k : Nat
Γ' : List VExpr
W : Ctx.LiftN n k Γ✝ Γ'
this :
  IsDefEq env U Γ' (lam (liftN n A✝ k) (app (lift (liftN n e✝ k)) (VExpr.bvar 0))) (liftN n e✝ k)
    (VExpr.forallE (liftN n A✝ k) (liftN n B✝ (k + 1)))
⊢ IsDefEq env U Γ' (liftN n (lam A✝ (app (lift e✝) (VExpr.bvar 0))) k) (liftN n e✝ k) (liftN n (VExpr.forallE A✝ B✝) k)

State before:
case eta
env : VEnv
henv : Ordered env
n : Nat
Γ : List VExpr
U : Nat
e1 e2 A : VExpr
Γ✝ : List VExpr
e✝ A✝ B✝ : VExpr
a✝ : IsDefEq env U Γ✝ e✝ e✝ (VExpr.forallE A✝ B✝)
ih :
  ∀ {k : Nat} {Γ' : List VExpr},
    Ctx.LiftN n k Γ✝ Γ' → IsDefEq env U Γ' (liftN n e✝ k) (liftN n e✝ k) (liftN n (VExpr.forallE A✝ B✝) k)
k : Nat
Γ' : List VExpr
W : Ctx.LiftN n k Γ✝ Γ'
this :
  IsDefEq env U Γ' (lam (liftN n A✝ k) (app (lift (liftN n e✝ k)) (VExpr.bvar 0))) (liftN n e✝ k)
    (VExpr.forallE (liftN n A✝ k) (liftN n B✝ (k + 1)))
⊢ IsDefEq env U Γ' (liftN n (lam A✝ (app (lift e✝) (VExpr.bvar 0))) k) (liftN n e✝ k) (liftN n (VExpr.forallE A✝ B✝) k)
Tactic:
simp [liftN]
State after:
case eta
env : VEnv
henv : Ordered env
n : Nat
Γ : List VExpr
U : Nat
e1 e2 A : VExpr
Γ✝ : List VExpr
e✝ A✝ B✝ : VExpr
a✝ : IsDefEq env U Γ✝ e✝ e✝ (VExpr.forallE A✝ B✝)
ih :
  ∀ {k : Nat} {Γ' : List VExpr},
    Ctx.LiftN n k Γ✝ Γ' → IsDefEq env U Γ' (liftN n e✝ k) (liftN n e✝ k) (liftN n (VExpr.forallE A✝ B✝) k)
k : Nat
Γ' : List VExpr
W : Ctx.LiftN n k Γ✝ Γ'
this :
  IsDefEq env U Γ' (lam (liftN n A✝ k) (app (lift (liftN n e✝ k)) (VExpr.bvar 0))) (liftN n e✝ k)
    (VExpr.forallE (liftN n A✝ k) (liftN n B✝ (k + 1)))
⊢ IsDefEq env U Γ' (lam (liftN n A✝ k) (app (liftN n (lift e✝) (k + 1)) (VExpr.bvar 0))) (liftN n e✝ k)
    (VExpr.forallE (liftN n A✝ k) (liftN n B✝ (k + 1)))

State before:
case eta
env : VEnv
henv : Ordered env
n : Nat
Γ : List VExpr
U : Nat
e1 e2 A : VExpr
Γ✝ : List VExpr
e✝ A✝ B✝ : VExpr
a✝ : IsDefEq env U Γ✝ e✝ e✝ (VExpr.forallE A✝ B✝)
ih :
  ∀ {k : Nat} {Γ' : List VExpr},
    Ctx.LiftN n k Γ✝ Γ' → IsDefEq env U Γ' (liftN n e✝ k) (liftN n e✝ k) (liftN n (VExpr.forallE A✝ B✝) k)
k : Nat
Γ' : List VExpr
W : Ctx.LiftN n k Γ✝ Γ'
this :
  IsDefEq env U Γ' (lam (liftN n A✝ k) (app (lift (liftN n e✝ k)) (VExpr.bvar 0))) (liftN n e✝ k)
    (VExpr.forallE (liftN n A✝ k) (liftN n B✝ (k + 1)))
⊢ IsDefEq env U Γ' (lam (liftN n A✝ k) (app (liftN n (lift e✝) (k + 1)) (VExpr.bvar 0))) (liftN n e✝ k)
    (VExpr.forallE (liftN n A✝ k) (liftN n B✝ (k + 1)))
Tactic:
rwa [← lift_liftN']
State after:
no goals

State before:
case proofIrrel
env : VEnv
henv : Ordered env
n : Nat
Γ : List VExpr
U : Nat
e1 e2 A : VExpr
Γ✝ : List VExpr
p✝ h✝ h'✝ : VExpr
a✝² : IsDefEq env U Γ✝ p✝ p✝ (VExpr.sort VLevel.zero)
a✝¹ : IsDefEq env U Γ✝ h✝ h✝ p✝
a✝ : IsDefEq env U Γ✝ h'✝ h'✝ p✝
ih1 :
  ∀ {k : Nat} {Γ' : List VExpr},
    Ctx.LiftN n k Γ✝ Γ' → IsDefEq env U Γ' (liftN n p✝ k) (liftN n p✝ k) (liftN n (VExpr.sort VLevel.zero) k)
ih2 : ∀ {k : Nat} {Γ' : List VExpr}, Ctx.LiftN n k Γ✝ Γ' → IsDefEq env U Γ' (liftN n h✝ k) (liftN n h✝ k) (liftN n p✝ k)
ih3 :
  ∀ {k : Nat} {Γ' : List VExpr}, Ctx.LiftN n k Γ✝ Γ' → IsDefEq env U Γ' (liftN n h'✝ k) (liftN n h'✝ k) (liftN n p✝ k)
k : Nat
Γ' : List VExpr
W : Ctx.LiftN n k Γ✝ Γ'
⊢ IsDefEq env U Γ' (liftN n h✝ k) (liftN n h'✝ k) (liftN n p✝ k)
Tactic:
exact .proofIrrel (ih1 W) (ih2 W) (ih3 W)
State after:
no goals

State before:
case extra
env : VEnv
henv : Ordered env
n : Nat
Γ : List VExpr
U : Nat
e1 e2 A : VExpr
df✝ : VDefEq
ls✝ : List VLevel
Γ✝ : List VExpr
h1 : env.defeqs df✝
h2 : ∀ (l : VLevel), l ∈ ls✝ → VLevel.WF U l
h3 : List.length ls✝ = df✝.uvars
k : Nat
Γ' : List VExpr
W : Ctx.LiftN n k Γ✝ Γ'
⊢ IsDefEq env U Γ' (liftN n (instL ls✝ df✝.lhs) k) (liftN n (instL ls✝ df✝.rhs) k) (liftN n (instL ls✝ df✝.type) k)
Tactic:
have ⟨⟨hA1, _⟩, hA2, hA3⟩ := henv.closed.2 h1
State after:
case extra
env : VEnv
henv : Ordered env
n : Nat
Γ : List VExpr
U : Nat
e1 e2 A : VExpr
df✝ : VDefEq
ls✝ : List VLevel
Γ✝ : List VExpr
h1 : env.defeqs df✝
h2 : ∀ (l : VLevel), l ∈ ls✝ → VLevel.WF U l
h3 : List.length ls✝ = df✝.uvars
k : Nat
Γ' : List VExpr
W : Ctx.LiftN n k Γ✝ Γ'
hA1 : ClosedN df✝.lhs
right✝ : ClosedN df✝.type
hA2 : ClosedN df✝.rhs
hA3 : ClosedN df✝.type
⊢ IsDefEq env U Γ' (liftN n (instL ls✝ df✝.lhs) k) (liftN n (instL ls✝ df✝.rhs) k) (liftN n (instL ls✝ df✝.type) k)

State before:
case extra
env : VEnv
henv : Ordered env
n : Nat
Γ : List VExpr
U : Nat
e1 e2 A : VExpr
df✝ : VDefEq
ls✝ : List VLevel
Γ✝ : List VExpr
h1 : env.defeqs df✝
h2 : ∀ (l : VLevel), l ∈ ls✝ → VLevel.WF U l
h3 : List.length ls✝ = df✝.uvars
k : Nat
Γ' : List VExpr
W : Ctx.LiftN n k Γ✝ Γ'
hA1 : ClosedN df✝.lhs
right✝ : ClosedN df✝.type
hA2 : ClosedN df✝.rhs
hA3 : ClosedN df✝.type
⊢ IsDefEq env U Γ' (liftN n (instL ls✝ df✝.lhs) k) (liftN n (instL ls✝ df✝.rhs) k) (liftN n (instL ls✝ df✝.type) k)
Tactic:
rw [
  hA1.instL.liftN_eq (Nat.zero_le _),
  hA2.instL.liftN_eq (Nat.zero_le _),
  hA3.instL.liftN_eq (Nat.zero_le _)]
State after:
case extra
env : VEnv
henv : Ordered env
n : Nat
Γ : List VExpr
U : Nat
e1 e2 A : VExpr
df✝ : VDefEq
ls✝ : List VLevel
Γ✝ : List VExpr
h1 : env.defeqs df✝
h2 : ∀ (l : VLevel), l ∈ ls✝ → VLevel.WF U l
h3 : List.length ls✝ = df✝.uvars
k : Nat
Γ' : List VExpr
W : Ctx.LiftN n k Γ✝ Γ'
hA1 : ClosedN df✝.lhs
right✝ : ClosedN df✝.type
hA2 : ClosedN df✝.rhs
hA3 : ClosedN df✝.type
⊢ IsDefEq env U Γ' (instL ls✝ df✝.lhs) (instL ls✝ df✝.rhs) (instL ls✝ df✝.type)

State before:
case extra
env : VEnv
henv : Ordered env
n : Nat
Γ : List VExpr
U : Nat
e1 e2 A : VExpr
df✝ : VDefEq
ls✝ : List VLevel
Γ✝ : List VExpr
h1 : env.defeqs df✝
h2 : ∀ (l : VLevel), l ∈ ls✝ → VLevel.WF U l
h3 : List.length ls✝ = df✝.uvars
k : Nat
Γ' : List VExpr
W : Ctx.LiftN n k Γ✝ Γ'
hA1 : ClosedN df✝.lhs
right✝ : ClosedN df✝.type
hA2 : ClosedN df✝.rhs
hA3 : ClosedN df✝.type
⊢ IsDefEq env U Γ' (instL ls✝ df✝.lhs) (instL ls✝ df✝.rhs) (instL ls✝ df✝.type)
Tactic:
exact .extra h1 h2 h3
State after:
no goals