def bs0

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64next.bend:315

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/f64.bend as SF
import bend-collections-laws-math@1.0.0.0/src/math/f64.bend as F
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/lib/word.bend as WD
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/f64bits.bend as FB

315# from a zero: the smallest subnormal with y's sign
316def bs0(+one: Nat, +h1: {one == 1n : Nat}, +s: Bool, +c: U32, +hc: {c == U32{WD.pw(32n, 31n)} : U32}) -> {F.Bits{U32.from_nat(1n), U32.from_nat(C.shift(31n, SF.pick(Nat, s, one, 0n)))} == F.Bits{1, SF.pick(U32, s, c, 0)} : F.F64}:
317  match s:
318    case True{}:
319      Equal.cong(U32, F.F64, z => F.Bits{U32.from_nat(1n), z}, U32.from_nat(C.shift(31n, one)), c, Equal.trans(U32, U32.from_nat(C.shift(31n, one)), U32.from_nat(v(c)), c, Equal.cong(Nat, U32, z => U32.from_nat(z), C.shift(31n, one), v(c), Equal.sym(Nat, v(c), C.shift(31n, one), FB.pwv(31n, {==}, one, h1, c, hc))), LW.rt(c)))
320    case False{}:
321      {==}