Theorem: Set.HAdd.hAdd.arg_a1.preimage_rule_Ioo (SciLean/Core/FunctionTransformations/Preimage.lean)

State before:
α : Type ?u.15024
β : Type ?u.15027
γ : Type ?u.15030
R : Type u_1
inst✝ : RealScalar R
x' a b : R
⊢ (fun x => x' + x) ⁻¹' Ioo a b = Ioo (a - x') (b - x')
Tactic:
ext
State after:
case h
α : Type ?u.15024
β : Type ?u.15027
γ : Type ?u.15030
R : Type u_1
inst✝ : RealScalar R
x' a b x✝ : R
⊢ x✝ ∈ (fun x => x' + x) ⁻¹' Ioo a b ↔ x✝ ∈ Ioo (a - x') (b - x')

State before:
case h
α : Type ?u.15024
β : Type ?u.15027
γ : Type ?u.15030
R : Type u_1
inst✝ : RealScalar R
x' a b x✝ : R
⊢ x✝ ∈ (fun x => x' + x) ⁻¹' Ioo a b ↔ x✝ ∈ Ioo (a - x') (b - x')
Tactic:
simp
State after:
case h
α : Type ?u.15024
β : Type ?u.15027
γ : Type ?u.15030
R : Type u_1
inst✝ : RealScalar R
x' a b x✝ : R
⊢ a < x' + x✝ ∧ x' + x✝ < b ↔ a - x' < x✝ ∧ x✝ < b - x'

State before:
case h
α : Type ?u.15024
β : Type ?u.15027
γ : Type ?u.15030
R : Type u_1
inst✝ : RealScalar R
x' a b x✝ : R
⊢ a < x' + x✝ ∧ x' + x✝ < b ↔ a - x' < x✝ ∧ x✝ < b - x'
Tactic:
sorry_proof
State after:
no goals