Nat.div2_step: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as Nat
Lines 510-515 of bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&start_line=510&end_line=515

import Base

def div2_step(+i: Nat) -> {Nat.div(Nat.add(2n, i), 2n) == 1n+Nat.div(i, 2n) : Nat}:
  Equal.trans(Nat, Pair.fst(Nat, Nat, Nat.divmod.go(Nat.add(2n, i), 1n, 0n, 0n)), Pair.fst(Nat, Nat, bump2(Nat.divmod.go(i, 1n, 0n, 0n))), 1n+Pair.fst(Nat, Nat, Nat.divmod.go(i, 1n, 0n, 0n)),
    Equal.cong(Nat & Nat, Nat, pq => Pair.fst(Nat, Nat, pq), Nat.divmod.go(Nat.add(2n, i), 1n, 0n, 0n), bump2(Nat.divmod.go(i, 1n, 0n, 0n)),
      Equal.trans(Nat & Nat, Nat.divmod.go(Nat.add(2n, i), 1n, 0n, 0n), Nat.divmod.go(i, 1n, 1n, 0n), bump2(Nat.divmod.go(i, 1n, 0n, 0n)),
        peel2(i, 0n), acc2(i, 1n, 0n, 0n))),
    fst_bump2(Nat.divmod.go(i, 1n, 0n, 0n)))

Uses (12):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  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.div
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.divmod.go
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Pair
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Pair.fst
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=acc2
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=bump2
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=fst_bump2
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=peel2