Theorem: LO.FirstOrder.Rew.embSubsts_bv (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 : Rew L ξ₁ n₁ ξ₂ n₂
m : ℕ
t : Semiterm L Empty n
v : Fin n → Semiterm L ξ m
⊢ ((embSubsts v) t).bv = t.bv.biUnion fun i => (v i).bv
Tactic:
induction t <;> simp [Rew.func, Semiterm.bv_func, Finset.biUnion_biUnion, *]
State after:
case fvar
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 : Rew L ξ₁ n₁ ξ₂ n₂
m : ℕ
v : Fin n → Semiterm L ξ m
a✝ : Empty
⊢ ((embSubsts v) &a✝).bv = ∅

State before:
case fvar
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 : Rew L ξ₁ n₁ ξ₂ n₂
m : ℕ
v : Fin n → Semiterm L ξ m
a✝ : Empty
⊢ ((embSubsts v) &a✝).bv = ∅
Tactic:
contradiction
State after:
no goals