def div_value

bend-collections-laws-crypto@1.0.0.0 · proofs/math/u64/u64div.bend:273

import Base
import bend-collections-laws-crypto@1.0.0.0/src/math/u64.bend as U
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32div.bend as UD
import bend-collections-laws-crypto@1.0.0.0/proofs/math/u64/u64.bend as P

273# THEOREM: div_small is Nat division of the 64-bit value, for 0 < d <= 2^20.
274def div_value(+a: U.U64, +d: U32, +hd0: {U32.is_zero(d) == False{} : Bool}, +hle: {U32.is_le(d, 1048576) == True{} : Bool}) -> {P.val(U.div_small(a, d)) == Nat.div(P.val(a), UD.v(d)) : Nat}:
275  match a:
276    case U.U64{+lo, +hi}:
277      gval(1n, {==}, lo, hi, d, 1048576, 4096, 256, 4095, 255, hd0, hle, {==}, {==}, {==}, {==}, {==}, {==}, {==})