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

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

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

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