def which1

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/poly1305/final.bend:311

import Base
import bend-collections-laws-crypto@1.0.0.0/src/crypto/poly1305/limbs.bend as Li
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32.bend as U3
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/poly1305/arith.bend as A
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/poly1305/value.bend as V
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/poly1305/step.bend as ST

311def which1(+one: Nat, +h1: {one == 1n : Nat}, +h: List<&2, U32>, +hh: {ST.inv(h) == True{} : Bool}, +hc: {Nat.is_eq(qq(h), 0n) == False{} : Bool}) -> {Li.freeze(h) == Li.take(16n, gg(h)) : List<&2, U32>}:
312  +eb = U3.injective(bb(h), 1, A.tr(V.v(bb(h)), qq(h), 1n, bval(one, h1, h, hh), qone(one, h1, h, hh, hc)))
313  Equal.trans(List<&2, U32>, Li.freeze(h), Li.select(U32.sub(0, 1), Li.take(16n, h), Li.take(16n, gg(h))), Li.take(16n, gg(h)),
314    Equal.cong(U32, List<&2, U32>, w => Li.select(U32.sub(0, w), Li.take(16n, h), Li.take(16n, gg(h))), bb(h), 1, eb),
315    sel1(Li.take(16n, h), Li.take(16n, gg(h)), heqlen(h, hh)))