Theorem: LO.FirstOrder.Semiterm.fvarList_empty (Logic/FirstOrder/Basic/Syntax/Term.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
inst✝ : DecidableEq ξ
o : Type u_6
e : IsEmpty o
t : Semiterm L o n
⊢ t.fvarList = []
Tactic:
induction t <;> simp[List.eq_nil_iff_forall_not_mem]
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
inst✝ : DecidableEq ξ
o : Type u_6
e : IsEmpty o
a✝ : o
⊢ False

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
inst✝ : DecidableEq ξ
o : Type u_6
e : IsEmpty o
x : o
⊢ False
Tactic:
case fvar x => exact IsEmpty.elim e x
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
inst✝ : DecidableEq ξ
o : Type u_6
e : IsEmpty o
x : o
⊢ False
Tactic:
exact IsEmpty.elim e x
State after:
no goals