R : Type u
inst✝ : LinearOrder R
x y z : Tropical R
⊢ min (untrop x) (untrop y) = untrop z ↔ x = z ∧ x ≤ y ∨ y = z ∧ y ≤ x
R : Type u
inst✝ : LinearOrder R
x y z : Tropical R
⊢ x + y = z ↔ x = z ∧ x ≤ y ∨ y = z ∧ y ≤ x
rw [trop_add_def, trop_eq_iff_eq_untrop]
no goals
R : Type u
inst✝ : LinearOrder R
x y z : Tropical R
⊢ min (untrop x) (untrop y) = untrop z ↔ x = z ∧ x ≤ y ∨ y = z ∧ y ≤ x
simp [min_eq_iff]