def sub32

bend-collections-laws-math@1.0.0.0 · proofs/lib/u32div.bend:70

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

70def sub32(+one: Nat, +h1: {one == 1n : Nat}, +x: U32, +b: U32, +d: Nat, +e: {Nat.add(v(x), WD.sc(32n, one)) == Nat.add(d, v(b)) : Nat}, +hd: {Nat.is_lt(d, WD.sc(32n, one)) == True{} : Bool}) -> {v(U32.sub(x, b)) == d : Nat}:
71  match x b:
72    case U32{+xw} U32{+bw}:
73      +e2 = Equal.trans(Nat, Nat.add(WD.uw(32n, xw), WD.sc(32n, one)), Nat.add(v(U32{xw}), WD.sc(32n, one)), Nat.add(d, WD.uw(32n, bw)),
74        Equal.cong(Nat, Nat, z => Nat.add(z, WD.sc(32n, one)), WD.uw(32n, xw), v(U32{xw}), Equal.sym(Nat, v(U32{xw}), WD.uw(32n, xw), vw(xw))),
75        Equal.trans(Nat, Nat.add(v(U32{xw}), WD.sc(32n, one)), Nat.add(d, v(U32{bw})), Nat.add(d, WD.uw(32n, bw)), e, Equal.cong(Nat, Nat, z => Nat.add(d, z), v(U32{bw}), WD.uw(32n, bw), vw(bw))))
76      %Equal.sym(Nat, v(U32{Word.sub(32n, xw, bw)}), WD.uw(32n, Word.sub(32n, xw, bw)), vw(Word.sub(32n, xw, bw))) : {_ == d : Nat}
77      WD.sub_wrap(32n, one, h1, xw, bw, d, e2, hd)