Theorem: LO.FirstOrder.Rew.q_toS (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
⊢ toS.q = bind ![#0] fun x => #x.succ
Tactic:
ext x <;> simp
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
x : Fin (0 + 1)
⊢ x = 0

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
x : Fin (0 + 1)
⊢ x = 0
Tactic:
cases x using Fin.cases <;> try simp
State after:
case hb.succ
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
i✝ : Fin 0
⊢ i✝.succ = 0

State before:
case hb.zero
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
⊢ 0 = 0
Tactic:
simp
State after:
no goals

State before:
case hb.succ
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
i✝ : Fin 0
⊢ i✝.succ = 0
Tactic:
exact Fin.elim0 (by assumption)
State after:
no goals

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
i✝ : Fin 0
⊢ Fin 0
Tactic:
assumption
State after:
no goals