Uint64n.pred_value: 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 94-99 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=94&end_line=99

import Base
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/lib/nat.bend as N
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64add.bend as WA

# n - 1 for a nonzero n
def pred_value(+n: WU.U64, +m: Nat, +hv: {SW.value(n) == 1n+m : Nat}) -> {SW.value(X.sub(n, one64())) == m : Nat}:
  +hle = Equal.trans(Bool, Nat.is_le(1n, SW.value(n)), Nat.is_le(1n, 1n+m), True{}, Equal.cong(Nat, Bool, z => Nat.is_le(1n, z), SW.value(n), 1n+m, hv), N.zero_le(m))
  Equal.trans(Nat, SW.value(X.sub(n, one64())), Nat.sub(SW.value(n), 1n), m, WA.sub_value(n, one64(), hle),
    %Equal.sym(Nat, SW.value(n), 1n+m, hv) : {Nat.sub(_, 1n) == m : Nat}
    N.sub_zero(m))

Uses (14):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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.sym
  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.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=sub_zero
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=zero_le
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/uint64n.bend&name=one64
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64add.bend&name=sub_value
  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=sub