def le_signed

bend-collections-laws-math@1.0.0.0 · proofs/math/u64/u64.bend:116

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

116# THEOREM: le_signed is the specification's signed 64-bit order.
117def 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}:
118  match a b:
119    case U.U64{alo, ahi} U.U64{blo, bhi}:
120      %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}
121      %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}
122      le_sign_spec(alo, ahi, blo, bhi, U32.is_ge(ahi, 2147483648), U32.is_ge(bhi, 2147483648))