U32and.andm: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/u32and.bend as U32and
Lines 42-44 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/u32and.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/u32and.bend&start_line=42&end_line=44

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as C
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/word.bend as WD

# x and c for a mask constant c = 2^k - 1
def andm(+x: U32, +k: Nat, +c: U32, +hc: {c == U32{WD.mask(32n, k)} : U32}) -> {v(U32.and(x, c)) == C.low(k, v(x)) : Nat}:
  L.subst(U32, z => {v(U32.and(x, z)) == C.low(k, v(x)) : Nat}, U32{WD.mask(32n, k)}, c, Equal.sym(U32, c, U32{WD.mask(32n, k)}, hc), andm0(x, k))

Uses (9):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.and
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/u32and.bend&name=andm0
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/u32and.bend&name=v
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend&name=subst
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend&name=mask
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=low