def and_le32

bend-collections-laws-math@1.0.0.0 · proofs/math/hash/hash.bend:38

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/word.bend as WD
import bend-collections-laws-math@1.0.0.0/proofs/lib/u32div.bend as UD

38def and_le32(+x: U32, +m: U32) -> {Nat.is_le(UD.v(U32.and(x, m)), UD.v(m)) == True{} : Bool}:
39  match x m:
40    case U32{+a} U32{+b}:
41      %Equal.sym(Nat, UD.v(U32{Word.and(32n, a, b)}), WD.uw(32n, Word.and(32n, a, b)), UD.vw(Word.and(32n, a, b))) : {Nat.is_le(_, UD.v(U32{b})) == True{} : Bool}
42      %Equal.sym(Nat, UD.v(U32{b}), WD.uw(32n, b), UD.vw(b)) : {Nat.is_le(WD.uw(32n, Word.and(32n, a, b)), _) == True{} : Bool}
43      and_le(32n, a, b)