Theorem: Pos.le_of_mul_le_mul_right (Extra/Pos/Lemmas.lean)

State before:
x y z : Pos
⊢ x * z ≤ y * z → x ≤ y
Tactic:
by_toNat
State after:
x y z : Pos
⊢ y.toNat * z.toNat ≥ x.toNat * z.toNat → y.toNat ≥ x.toNat

State before:
x y z : Pos
⊢ y.toNat * z.toNat ≥ x.toNat * z.toNat → y.toNat ≥ x.toNat
Tactic:
intro h
State after:
x y z : Pos
h : y.toNat * z.toNat ≥ x.toNat * z.toNat
⊢ y.toNat ≥ x.toNat

State before:
x y z : Pos
h : y.toNat * z.toNat ≥ x.toNat * z.toNat
⊢ y.toNat ≥ x.toNat
Tactic:
exact Nat.le_of_mul_le_mul_of_pos_right (Nat.zero_lt _) h
State after:
no goals