def select0

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/curve25519/fieldops.bend:184

import Base
import bend-collections-laws-crypto@1.0.0.0/src/crypto/curve25519/field.bend as F
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend as L
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32alg.bend as A
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/limbs.bend as LM

184def select0(+one: Nat, +h1: {one == 1n : Nat}, +n: Nat, +xs: List<&2, U32>, +ys: List<&2, U32>, +hx: {LM.okb(n, xs, 255n) == True{} : Bool}, +hy: {LM.okb(n, ys, 255n) == True{} : Bool}) -> {F.select(0, xs, ys) == xs : List<&2, U32>}:
185  match n xs ys:
186    case 0n Nil{} _:
187      {==}
188    case 0n Con{x, xt} _:
189      Empty.absurd({F.select(0, Con{x, xt}, ys) == Con{x, xt} : List<&2, U32>}, L.false_true(hx))
190    case 1n+m Nil{} _:
191      {==}
192    case 1n+m Con{x, xt} Nil{}:
193      Empty.absurd({Nil{} == Con{x, xt} : List<&2, U32>}, L.false_true(hy))
194    case 1n+ +m Con{+x, +xt} Con{+y, +yt}:
195      +e1 = Equal.trans(U32, U32.add(U32.mul(x, 1), U32.mul(y, 0)), U32.add(x, U32.mul(y, 0)), x, Equal.cong(U32, U32, z => U32.add(z, U32.mul(y, 0)), U32.mul(x, 1), x, mul1(one, h1, x)) , Equal.trans(U32, U32.add(x, U32.mul(y, 0)), U32.add(x, 0), x, Equal.cong(U32, U32, z => U32.add(x, z), U32.mul(y, 0), 0, mul0(one, h1, y)), A.add_zero(x)))
196      +e2 = select0(one, h1, m, xt, yt, LM.okb_tail(m, x, xt, 255n, hx), LM.okb_tail(m, y, yt, 255n, hy))
197      Equal.trans(List<&2, U32>, Con{U32.add(U32.mul(x, 1), U32.mul(y, 0)), F.select(0, xt, yt)}, Con{x, F.select(0, xt, yt)}, Con{x, xt}, Equal.cong(U32, List<&2, U32>, z => Con{z, F.select(0, xt, yt)}, U32.add(U32.mul(x, 1), U32.mul(y, 0)), x, e1), Equal.cong(List<&2, U32>, List<&2, U32>, z => Con{x, z}, F.select(0, xt, yt), xt, e2))