have habax : a*b' = a*c' := add_right_cancel h
case a
a : Nat
ha : a ≠ zero
b' : Nat
ihb : ∀ (c : Nat), a * b' = a * c → b' = c
x✝ c' : Nat
h : a * b' + a = a * c' + a
⊢ b' = c'
case a
a : Nat
ha : a ≠ zero
b' : Nat
ihb : ∀ (c : Nat), a * b' = a * c → b' = c
x✝ c' : Nat
h : a * b' + a = a * c' + a
habax : a * b' = a * c'
⊢ b' = c'