def zero_pair

bend-collections-laws-math@1.0.0.0 · proofs/math/random/uint64n.bend:282

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/spec/math/random/source.bend as SRC
import bend-collections-laws-math@1.0.0.0/src/math/u64.bend as WU
import bend-collections-laws-math@1.0.0.0/src/math/w64.bend as X
import bend-collections-laws-math@1.0.0.0/src/math/random/rand.bend as R
import bend-collections-laws-math@1.0.0.0/spec/math/random.bend as SRM

282# n == 0 is read as 2^64: the whole word
283def zero_pair(-S: Data, p: WU.U64 & S) -> {SRM.val_pair(S, R.mask(S, Z(), p)) == (SW.value(SRC.fst64(S, p)), SRC.snd64(S, p)) : Nat & S}:
284  match p:
285    case Tuple{+x, +s1}:
286      match x:
287        case WU.U64{+l, +h}:
288          %Equal.sym(U32, U32.and(l, X.lo(X.sub(Z(), one64()))), l, uand_all(l, X.lo(X.sub(Z(), one64())), {==})) : {(Nat.add(U32.to_nat(_), C.shift(32n, U32.to_nat(U32.and(h, X.hi(X.sub(Z(), one64())))))), s1) == (SW.value(WU.U64{l, h}), s1) : Nat & S}
289          %Equal.sym(U32, U32.and(h, X.hi(X.sub(Z(), one64()))), h, uand_all(h, X.hi(X.sub(Z(), one64())), {==})) : {(Nat.add(U32.to_nat(l), C.shift(32n, U32.to_nat(_))), s1) == (SW.value(WU.U64{l, h}), s1) : Nat & S}
290          {==}