Float.exp_amt0: 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 50-57 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=50&end_line=57

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

# the exponent field of the implementation: 1033 - clz = 970 + j
def exp_amt0(+j: Nat, +hj: {Nat.is_le(j, 52n) == True{} : Bool}) -> {Nat.sub(1033n, Nat.sub(63n, j)) == Nat.add(970n, j) : Nat}:
  +r = Nat.sub(52n, j)
  +e1 = N.sub_add(52n, j, hj)
  +e3 = Equal.trans(Nat, Nat.add(r, Nat.add(970n, j)), Nat.add(Nat.add(970n, j), r), 1022n, N.add_comm(r, Nat.add(970n, j)), Equal.cong(Nat, Nat, z => Nat.add(970n, z), Nat.add(j, r), 52n, e1))
  %Equal.sym(Nat, Nat.sub(63n, j), Nat.add(11n, r), sub63(j, hj)) : {Nat.sub(1033n, _) == Nat.add(970n, j) : Nat}
  %e3 : {Nat.sub(_, r) == Nat.add(970n, j) : Nat}
  N.add_sub_cancel(r, Nat.add(970n, j))

Uses (12):
  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.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
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/float.bend&name=sub63