Uint64n.m128_hi: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/random/uint64n.bend as Uint64n
Lines 125-131 of bend-collections-laws-math@1.0.0.0/proofs/math/random/uint64n.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/uint64n.bend&start_line=125&end_line=131

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/u64.bend as WU
import bend-collections-laws-math@1.0.0.0/src/math/w64.bend as X
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/width.bend as WI
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64m128.bend as M128

def m128_hi(+x: WU.U64, +n: WU.U64) -> {SW.value(X.psnd(X.mul128(x, n))) == C.high(64n, Nat.mul(SW.value(x), SW.value(n))) : Nat}:
  match x n:
    case WU.U64{+al, +ah} WU.U64{+bl, +bh}:
      +r = SW.value(X.pfst(X.mul128(WU.U64{al, ah}, WU.U64{bl, bh})))
      +q = SW.value(X.psnd(X.mul128(WU.U64{al, ah}, WU.U64{bl, bh})))
      %M128.m128_value(al, ah, bl, bh) : {q == C.high(64n, _) : Nat}
      Equal.sym(Nat, C.high(64n, Nat.add(r, C.shift(64n, q))), q, WI.high_u(64n, r, q, M128.fit64(X.pfst(X.mul128(WU.U64{al, ah}, WU.U64{bl, bh})))))

Uses (14):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64m128.bend&name=fit64
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64m128.bend&name=m128_value
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/width.bend&name=high_u
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=high
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=shift
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/w64.bend&name=value
  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/w64.bend&name=mul128
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/w64.bend&name=pfst
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/w64.bend&name=psnd