case mp
R : Type u_1
inst✝ : Rack R
x y y' : R
⊢ x ◃⁻¹ y = x ◃⁻¹ y' → y = y'

case mpr
R : Type u_1
inst✝ : Rack R
x y y' : R
⊢ y = y' → x ◃⁻¹ y = x ◃⁻¹ y'
R : Type u_1
inst✝ : Rack R
x y y' : R
⊢ x ◃⁻¹ y = x ◃⁻¹ y' ↔ y = y'
constructor
case mpr
R : Type u_1
inst✝ : Rack R
x y y' : R
⊢ y = y' → x ◃⁻¹ y = x ◃⁻¹ y'
case mp
R : Type u_1
inst✝ : Rack R
x y y' : R
⊢ x ◃⁻¹ y = x ◃⁻¹ y' → y = y'

case mpr
R : Type u_1
inst✝ : Rack R
x y y' : R
⊢ y = y' → x ◃⁻¹ y = x ◃⁻¹ y'
apply (act' x).symm.injective
case mpr
R : Type u_1
inst✝ : Rack R
x y : R
⊢ x ◃⁻¹ y = x ◃⁻¹ y
case mpr
R : Type u_1
inst✝ : Rack R
x y y' : R
⊢ y = y' → x ◃⁻¹ y = x ◃⁻¹ y'
rintro rfl
no goals
case mpr
R : Type u_1
inst✝ : Rack R
x y : R
⊢ x ◃⁻¹ y = x ◃⁻¹ y
rfl