def tval

bend-collections-laws-crypto@1.0.0.0 · proofs/math/u64/u64div.bend:184

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend as WD
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/arith.bend as AR
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32div.bend as UD

184# one digit of the long division: t = x * 2^j + y with x < d, y < 2^j
185def tval(+one: Nat, +h1: {one == 1n : Nat}, +j: Nat, +x: U32, +k: U32, +y: U32, +dn: Nat, +hk: {UD.v(k) == WD.sc(j, one) : Nat}, +hy: {Nat.is_lt(UD.v(y), WD.sc(j, one)) == True{} : Bool}, +hx: {Nat.is_lt(UD.v(x), dn) == True{} : Bool}, +hjk: {Nat.is_le(WD.sc(j, dn), WD.sc(32n, one)) == True{} : Bool}) -> {UD.v(U32.add(U32.mul(x, k), y)) == Nat.add(WD.sc(j, UD.v(x)), UD.v(y)) : Nat}:
186  +hm = N.lt_le_trans(WD.sc(j, UD.v(x)), WD.sc(j, dn), WD.sc(32n, one), AR.sc_lt(j, UD.v(x), dn, hx), hjk)
187  +ha = N.lt_le_trans(Nat.add(WD.sc(j, UD.v(x)), UD.v(y)), WD.sc(j, dn), WD.sc(32n, one), AR.digit_lt(j, one, h1, UD.v(y), UD.v(x), dn, hy, hx), hjk)
188  addv32(one, h1, U32.mul(x, k), y, WD.sc(j, UD.v(x)), UD.v(y), mulp32(one, h1, j, x, k, hk, hm), {==}, ha)