def vb_small

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/w64dmrem.bend:22

import Base
import bend-collections-laws-math@1.0.0.0/spec/lib/common.bend as C
import bend-collections-laws-math@1.0.0.0/spec/math/w64.bend as SW
import bend-collections-laws-math@1.0.0.0/src/math/u64.bend as WU
import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/width.bend as WW
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/u32laws.bend as LW
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64dm.bend as DM

22def vb_small(+bl: U32, +bh: U32, +hz: {U32.is_zero(bh) == True{} : Bool}) -> {SW.value(WU.U64{bl, bh}) == DM.v(bl) : Nat}:
23  +e0 = N.eq_from_is_eq(DM.v(bh), 0n, Equal.trans(Bool, Nat.is_eq(DM.v(bh), 0n), U32.is_zero(bh), True{}, Equal.sym(Bool, U32.is_zero(bh), Nat.is_eq(DM.v(bh), 0n), LW.zero_nat(bh)), hz))
24  Equal.trans(Nat, Nat.add(DM.v(bl), C.shift(32n, DM.v(bh))), Nat.add(DM.v(bl), C.shift(32n, 0n)), DM.v(bl), Equal.cong(Nat, Nat, z => Nat.add(DM.v(bl), C.shift(32n, z)), DM.v(bh), 0n, e0), Equal.trans(Nat, Nat.add(DM.v(bl), C.shift(32n, 0n)), Nat.add(DM.v(bl), 0n), DM.v(bl), Equal.cong(Nat, Nat, z => Nat.add(DM.v(bl), z), C.shift(32n, 0n), 0n, WW.shift_zero(32n)), N.add_zero(DM.v(bl))))