def mask_value

bend-collections-laws-crypto@1.0.0.0 · proofs/math/random/uint64n.bend:110

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/math/w64.bend as SW
import bend-collections-laws-crypto@1.0.0.0/spec/math/random/rand.bend as SR
import bend-collections-laws-crypto@1.0.0.0/src/math/u64.bend as WU
import bend-collections-laws-crypto@1.0.0.0/src/math/w64.bend as X
import bend-collections-laws-crypto@1.0.0.0/src/math/random/rand.bend as R
import bend-collections-laws-crypto@1.0.0.0/proofs/math/random/bits.bend as BI

110# the mask is x & (n - 1)
111def mask_value(+x: WU.U64, +n: WU.U64, +m: Nat, +hv: {SW.value(n) == 1n+m : Nat}) -> {SW.value(R.and64(x, X.sub(n, one64()))) == SR.and_bits(64n, SW.value(x), m) : Nat}:
112  %Equal.sym(Nat, SW.value(R.and64(x, X.sub(n, one64()))), SR.and_bits(64n, SW.value(x), SW.value(X.sub(n, one64()))), BI.and64_value(x, X.sub(n, one64()))) : {_ == SR.and_bits(64n, SW.value(x), m) : Nat}
113  %Equal.sym(Nat, SW.value(X.sub(n, one64())), m, pred_value(n, m, hv)) : {SR.and_bits(64n, SW.value(x), _) == SR.and_bits(64n, SW.value(x), m) : Nat}
114  {==}