Float.sub63: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/random/float.bend as Float
Lines 37-43 of bend-collections-laws-math@1.0.0.0/proofs/math/random/float.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/float.bend&start_line=37&end_line=43

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

# 63 - j = 11 + (52 - j)
def sub63(+j: Nat, +hj: {Nat.is_le(j, 52n) == True{} : Bool}) -> {Nat.sub(63n, j) == Nat.add(11n, Nat.sub(52n, j)) : Nat}:
  +r = Nat.sub(52n, j)
  +e1 = N.sub_add(52n, j, hj)
  +e2 = Equal.trans(Nat, Nat.add(j, Nat.add(11n, r)), Nat.add(Nat.add(11n, r), j), 63n, N.add_comm(j, Nat.add(11n, r)), Equal.cong(Nat, Nat, z => Nat.add(11n, z), Nat.add(r, j), 52n, Equal.trans(Nat, Nat.add(r, j), Nat.add(j, r), 52n, N.add_comm(r, j), e1)))
  %e2 : {Nat.sub(_, j) == Nat.add(11n, r) : Nat}
  N.add_sub_cancel(j, Nat.add(11n, r))

Uses (10):
  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.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.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=add_comm
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=add_sub_cancel
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=sub_add