def carry_of

bend-collections-laws-crypto@1.0.0.0 · proofs/math/typed/u32laws.bend:162

import Base
import bend-collections-laws-crypto@1.0.0.0/src/math/instances.bend as I
import bend-collections-laws-crypto@1.0.0.0/src/math/num.bend as NM
import bend-collections-laws-crypto@1.0.0.0/proofs/math/u64/u64.bend as P64

162def carry_of(+a: U32, +b: U32, +h: {I.u32_is(NM.AddOver{a, b}) == False{} : Bool}) -> {P64.carry32(a, b) == False{} : Bool}:
163  Equal.trans(Bool, P64.carry32(a, b), U32.is_lt(U32.add(a, b), a), False{}, Equal.sym(Bool, U32.is_lt(U32.add(a, b), a), P64.carry32(a, b), P64.add_lt(a, b)), h)