def wv.halves_eq

bend-osdev-word64@0.1.1.0 · proof_value.bend:363

import Base
import bend-osdev-u32@0.1.0.0/LAWS.bend as UL

363# equal values: equal halves
364def wv.halves_eq(+n: Nat, +ah: Word(n), +al: Word(n), +bh: Word(n), +bl: Word(n), e: {wv.V(n, ah, al) == wv.V(n, bh, bl) : Nat}) -> {(ah, al) == (bh, bl) : Word(n) & Word(n)}:
365  +c = Equal.trans(Cmp, wv.lex(Word.cmp(n, ah, bh), Word.cmp(n, al, bl)), Nat.cmp(wv.V(n, ah, al), wv.V(n, bh, bl)), EQ{}, wv.gcmp(n, ah, al, bh, bl), Equal.trans(Cmp, Nat.cmp(wv.V(n, ah, al), wv.V(n, bh, bl)), Nat.cmp(wv.V(n, bh, bl), wv.V(n, bh, bl)), EQ{}, Equal.cong(Nat, Cmp, v => Nat.cmp(v, wv.V(n, bh, bl)), wv.V(n, ah, al), wv.V(n, bh, bl), e), wn.cmp_refl(wv.V(n, bh, bl))))
366  +eh = UL.word_value_eq(n, ah, bh, wn.cmp_eq(Word.to_nat(n, ah), Word.to_nat(n, bh), Equal.trans(Cmp, Nat.cmp(Word.to_nat(n, ah), Word.to_nat(n, bh)), Word.cmp(n, ah, bh), EQ{}, Equal.sym(Cmp, Word.cmp(n, ah, bh), Nat.cmp(Word.to_nat(n, ah), Word.to_nat(n, bh)), UL.word_cmp_value(n, ah, bh)), wv.lex_eq_l(Word.cmp(n, ah, bh), Word.cmp(n, al, bl), c))))
367  +el = UL.word_value_eq(n, al, bl, wn.cmp_eq(Word.to_nat(n, al), Word.to_nat(n, bl), Equal.trans(Cmp, Nat.cmp(Word.to_nat(n, al), Word.to_nat(n, bl)), Word.cmp(n, al, bl), EQ{}, Equal.sym(Cmp, Word.cmp(n, al, bl), Nat.cmp(Word.to_nat(n, al), Word.to_nat(n, bl)), UL.word_cmp_value(n, al, bl)), wv.lex_eq_r(Word.cmp(n, ah, bh), Word.cmp(n, al, bl), c))))
368  %eh : {(ah, al) == (_, bl) : Word(n) & Word(n)}
369  %el : {(ah, al) == (ah, _) : Word(n) & Word(n)}
370  {==}