Theorem: LO.FirstOrder.Semiterm.Operator.positive_operator_iff (Logic/FirstOrder/Basic/Operator.lean)

State before:
L : Language
ξ : Type u_1
n k : ℕ
o : Operator L k
v : Fin k → Semiterm L ξ (n + 1)
⊢ (o.operator v).Positive ↔ ∀ i ∈ o.term.bv, (v i).Positive
Tactic:
simp [Positive, bv_operator]
State after:
L : Language
ξ : Type u_1
n k : ℕ
o : Operator L k
v : Fin k → Semiterm L ξ (n + 1)
⊢ (∀ (x : Fin (n + 1)), ∀ x_1 ∈ o.term.bv, x ∈ (v x_1).bv → 0 < x) ↔ ∀ i ∈ o.term.bv, ∀ x ∈ (v i).bv, 0 < x

State before:
L : Language
ξ : Type u_1
n k : ℕ
o : Operator L k
v : Fin k → Semiterm L ξ (n + 1)
⊢ (∀ (x : Fin (n + 1)), ∀ x_1 ∈ o.term.bv, x ∈ (v x_1).bv → 0 < x) ↔ ∀ i ∈ o.term.bv, ∀ x ∈ (v i).bv, 0 < x
Tactic:
exact ⟨fun h i hi x hx ↦ h x i hi hx, fun h x i hi hx ↦ h i hi x hx⟩
State after:
no goals