cases b
a b : binary
hb : b = binary.one ↔ a = binary.one
⊢ b = binary.zero ↔ a = binary.zero
case zero
a : binary
hb : binary.zero = binary.one ↔ a = binary.one
⊢ binary.zero = binary.zero ↔ a = binary.zero

case one
a : binary
hb : binary.one = binary.one ↔ a = binary.one
⊢ binary.one = binary.zero ↔ a = binary.zero