no goals
α : Type u_1
inst✝ : Field α
a b ad bd a' b' gcd : α
ha : ad * a = a'
hb : bd * b = b'
had : ad ≠ 0
hbd : bd ≠ 0
hgcd : gcd ≠ 0
⊢ (a ≠ b) = (1 / gcd * (bd * a') ≠ 1 / gcd * (ad * b'))
classical
rw [eq_iff_iff, not_iff_not, cancel_factors_eq ha hb had hbd hgcd]
no goals
α : Type u_1
inst✝ : Field α
a b ad bd a' b' gcd : α
ha : ad * a = a'
hb : bd * b = b'
had : ad ≠ 0
hbd : bd ≠ 0
hgcd : gcd ≠ 0
⊢ (a ≠ b) = (1 / gcd * (bd * a') ≠ 1 / gcd * (ad * b'))
rw [eq_iff_iff, not_iff_not, cancel_factors_eq ha hb had hbd hgcd]