Bounded.fst_val: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/random/bounded.bend as Bounded
Lines 16-19 of bend-collections-laws-math@1.0.0.0/proofs/math/random/bounded.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/bounded.bend&start_line=16&end_line=19

import Base
import bend-collections-laws-math@1.0.0.0/src/math/u64.bend as W
import bend-collections-laws-math@1.0.0.0/src/math/random/rand.bend as R
import bend-collections-laws-math@1.0.0.0/spec/math/w64.bend as SW
import bend-collections-laws-math@1.0.0.0/spec/math/random.bend as SRM
import bend-collections-laws-math@1.0.0.0/proofs/math/random/below.bend as BL

def fst_val(-S: Data, r: W.U64 & S) -> {BL.pfst(S, SRM.val_pair(S, r)) == SW.value(R.fst(W.U64, S, r)) : Nat}:
  match r:
    case Tuple{x, s}:
      {==}

Uses (8):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Pair
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Sigma
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/below.bend&name=pfst
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/math/random.bend&name=val_pair
  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/random/rand.bend&name=fst
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/src/math/u64.bend&name=U64