Theorem: LO.FirstOrder.Rew.q_rewrite (Logic/FirstOrder/Basic/Syntax/Rew.lean)

State before:
L : Language
L' : Language
L₁ : Language
L₂ : Language
L₃ : Language
ξ : Type u_1
ξ' : Type u_2
ξ₁ : Type u_3
ξ₂ : Type u_4
ξ₃ : Type u_5
n n₁ n₂ n₃ : ℕ
ω✝ ω : Rew L ξ₁ n₁ ξ₂ n₂
f : ξ₁ → Semiterm L ξ₂ n
⊢ (rewrite f).q = rewrite (⇑bShift ∘ f)
Tactic:
ext x
State after:
case hb
L : Language
L' : Language
L₁ : Language
L₂ : Language
L₃ : Language
ξ : Type u_1
ξ' : Type u_2
ξ₁ : Type u_3
ξ₂ : Type u_4
ξ₃ : Type u_5
n n₁ n₂ n₃ : ℕ
ω✝ ω : Rew L ξ₁ n₁ ξ₂ n₂
f : ξ₁ → Semiterm L ξ₂ n
x : Fin (n + 1)
⊢ (rewrite f).q #x = (rewrite (⇑bShift ∘ f)) #x

case hf
L : Language
L' : Language
L₁ : Language
L₂ : Language
L₃ : Language
ξ : Type u_1
ξ' : Type u_2
ξ₁ : Type u_3
ξ₂ : Type u_4
ξ₃ : Type u_5
n n₁ n₂ n₃ : ℕ
ω✝ ω : Rew L ξ₁ n₁ ξ₂ n₂
f : ξ₁ → Semiterm L ξ₂ n
x : ξ₁
⊢ (rewrite f).q &x = (rewrite (⇑bShift ∘ f)) &x

State before:
case hb
L : Language
L' : Language
L₁ : Language
L₂ : Language
L₃ : Language
ξ : Type u_1
ξ' : Type u_2
ξ₁ : Type u_3
ξ₂ : Type u_4
ξ₃ : Type u_5
n n₁ n₂ n₃ : ℕ
ω✝ ω : Rew L ξ₁ n₁ ξ₂ n₂
f : ξ₁ → Semiterm L ξ₂ n
x : Fin (n + 1)
⊢ (rewrite f).q #x = (rewrite (⇑bShift ∘ f)) #x

case hf
L : Language
L' : Language
L₁ : Language
L₂ : Language
L₃ : Language
ξ : Type u_1
ξ' : Type u_2
ξ₁ : Type u_3
ξ₂ : Type u_4
ξ₃ : Type u_5
n n₁ n₂ n₃ : ℕ
ω✝ ω : Rew L ξ₁ n₁ ξ₂ n₂
f : ξ₁ → Semiterm L ξ₂ n
x : ξ₁
⊢ (rewrite f).q &x = (rewrite (⇑bShift ∘ f)) &x
Tactic:
{ cases x using Fin.cases <;> simp[rewriteMap] }
State after:
case hf
L : Language
L' : Language
L₁ : Language
L₂ : Language
L₃ : Language
ξ : Type u_1
ξ' : Type u_2
ξ₁ : Type u_3
ξ₂ : Type u_4
ξ₃ : Type u_5
n n₁ n₂ n₃ : ℕ
ω✝ ω : Rew L ξ₁ n₁ ξ₂ n₂
f : ξ₁ → Semiterm L ξ₂ n
x : ξ₁
⊢ (rewrite f).q &x = (rewrite (⇑bShift ∘ f)) &x

State before:
case hf
L : Language
L' : Language
L₁ : Language
L₂ : Language
L₃ : Language
ξ : Type u_1
ξ' : Type u_2
ξ₁ : Type u_3
ξ₂ : Type u_4
ξ₃ : Type u_5
n n₁ n₂ n₃ : ℕ
ω✝ ω : Rew L ξ₁ n₁ ξ₂ n₂
f : ξ₁ → Semiterm L ξ₂ n
x : ξ₁
⊢ (rewrite f).q &x = (rewrite (⇑bShift ∘ f)) &x
Tactic:
{ simp }
State after:
no goals

State before:
case hb
L : Language
L' : Language
L₁ : Language
L₂ : Language
L₃ : Language
ξ : Type u_1
ξ' : Type u_2
ξ₁ : Type u_3
ξ₂ : Type u_4
ξ₃ : Type u_5
n n₁ n₂ n₃ : ℕ
ω✝ ω : Rew L ξ₁ n₁ ξ₂ n₂
f : ξ₁ → Semiterm L ξ₂ n
x : Fin (n + 1)
⊢ (rewrite f).q #x = (rewrite (⇑bShift ∘ f)) #x
Tactic:
cases x using Fin.cases <;> simp[rewriteMap]
State after:
no goals

State before:
case hf
L : Language
L' : Language
L₁ : Language
L₂ : Language
L₃ : Language
ξ : Type u_1
ξ' : Type u_2
ξ₁ : Type u_3
ξ₂ : Type u_4
ξ₃ : Type u_5
n n₁ n₂ n₃ : ℕ
ω✝ ω : Rew L ξ₁ n₁ ξ₂ n₂
f : ξ₁ → Semiterm L ξ₂ n
x : ξ₁
⊢ (rewrite f).q &x = (rewrite (⇑bShift ∘ f)) &x
Tactic:
simp
State after:
no goals