def or_le32

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/curve25519/xbits.bend:134

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

134def or_le32(+x: U32, +m: U32) -> {Nat.is_le(v(U32.or(x, m)), Nat.add(v(x), v(m))) == True{} : Bool}:
135  match x m:
136    case U32{+a} U32{+b}:
137      %Equal.sym(Nat, UD.v(U32{Word.or(32n, a, b)}), WD.uw(32n, Word.or(32n, a, b)), UD.vw(Word.or(32n, a, b))) : {Nat.is_le(_, Nat.add(v(U32{a}), v(U32{b}))) == True{} : Bool}
138      %Equal.sym(Nat, UD.v(U32{a}), WD.uw(32n, a), UD.vw(a)) : {Nat.is_le(WD.uw(32n, Word.or(32n, a, b)), Nat.add(_, v(U32{b}))) == True{} : Bool}
139      %Equal.sym(Nat, UD.v(U32{b}), WD.uw(32n, b), UD.vw(b)) : {Nat.is_le(WD.uw(32n, Word.or(32n, a, b)), Nat.add(WD.uw(32n, a), _)) == True{} : Bool}
140      or_le(32n, a, b)