def wval

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64bl.bend:39

import Base
import bend-collections-laws-math@1.0.0.0/spec/lib/common.bend as C
import bend-collections-laws-math@1.0.0.0/spec/math/w64.bend as SW
import bend-collections-laws-math@1.0.0.0/src/math/f64.bend as F
import bend-collections-laws-math@1.0.0.0/src/math/u64.bend as WU
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/width.bend as WW
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/u32laws.bend as LW
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64sh.bend as SH

39def wval(+n: Nat, +h64: {C.fits(64n, n) == True{} : Bool}) -> {SW.value(WU.U64{U32.from_nat(F.low_bits(32n, n)), U32.from_nat(F.high_bits(32n, n))}) == n : Nat}:
40  +el = Equal.trans(Nat, v(U32.from_nat(F.low_bits(32n, n))), v(U32.from_nat(C.low(32n, n))), C.low(32n, n), Equal.cong(Nat, Nat, z => v(U32.from_nat(z)), F.low_bits(32n, n), C.low(32n, n), lbits(32n, n)), LW.vo(C.low(32n, n), WW.low_fits(32n, n)))
41  +eh = Equal.trans(Nat, v(U32.from_nat(F.high_bits(32n, n))), v(U32.from_nat(C.high(32n, n))), C.high(32n, n), Equal.cong(Nat, Nat, z => v(U32.from_nat(z)), F.high_bits(32n, n), C.high(32n, n), hbits(32n, n)), LW.vo(C.high(32n, n), SH.fits_high(32n, 32n, n, h64)))
42  Equal.trans(Nat, Nat.add(v(U32.from_nat(F.low_bits(32n, n))), C.shift(32n, v(U32.from_nat(F.high_bits(32n, n))))), Nat.add(C.low(32n, n), C.shift(32n, v(U32.from_nat(F.high_bits(32n, n))))), n, Equal.cong(Nat, Nat, z => Nat.add(z, C.shift(32n, v(U32.from_nat(F.high_bits(32n, n))))), v(U32.from_nat(F.low_bits(32n, n))), C.low(32n, n), el), Equal.trans(Nat, Nat.add(C.low(32n, n), C.shift(32n, v(U32.from_nat(F.high_bits(32n, n))))), Nat.add(C.low(32n, n), C.shift(32n, C.high(32n, n))), n, Equal.cong(Nat, Nat, z => Nat.add(C.low(32n, n), C.shift(32n, z)), v(U32.from_nat(F.high_bits(32n, n))), C.high(32n, n), eh), Equal.sym(Nat, n, Nat.add(C.low(32n, n), C.shift(32n, C.high(32n, n))), WW.low_high(32n, n))))