U64.le_signed: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/u64/u64.bend as U64
Lines 116-122 of bend-collections-laws-math@1.0.0.0/proofs/math/u64/u64.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/u64/u64.bend&start_line=116&end_line=122

import Base
import bend-collections-laws-math@1.0.0.0/src/math/u64.bend as U
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/src/wide.bend as W
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/spec/numeric.bend as S

# THEOREM: le_signed is the specification's signed 64-bit order.
def le_signed(+a: U.U64, +b: U.U64) -> {U.le_signed(a, b) == S.order(bits(a), bits(b), S.negative(bits(a)), S.negative(bits(b))) : Bool}:
  match a b:
    case U.U64{alo, ahi} U.U64{blo, bhi}:
      %Equal.sym(Bool, S.negative(W.pack(alo, ahi)), U32.is_ge(ahi, 2147483648), negative_pack(alo, ahi)) : {U.le_signed(U.U64{alo, ahi}, U.U64{blo, bhi}) == S.order(W.pack(alo, ahi), W.pack(blo, bhi), _, S.negative(W.pack(blo, bhi))) : Bool}
      %Equal.sym(Bool, S.negative(W.pack(blo, bhi)), U32.is_ge(bhi, 2147483648), negative_pack(blo, bhi)) : {U.le_signed(U.U64{alo, ahi}, U.U64{blo, bhi}) == S.order(W.pack(alo, ahi), W.pack(blo, bhi), U32.is_ge(ahi, 2147483648), _) : Bool}
      le_sign_spec(alo, ahi, blo, bhi, U32.is_ge(ahi, 2147483648), U32.is_ge(bhi, 2147483648))

Uses (11):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_ge
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/spec/numeric.bend&name=negative
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/spec/numeric.bend&name=order
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/src/wide.bend&name=pack
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/u64/u64.bend&name=bits
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/u64/u64.bend&name=le_sign_spec
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/u64/u64.bend&name=negative_pack
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/u64.bend&name=U64
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/u64.bend&name=le_signed