Float.fits_up: 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 68-72 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=68&end_line=72

import Base
import bend-collections-laws-math@1.0.0.0/spec/lib/common.bend as C
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/width.bend as WW

def fits_up(+a: Nat, +d: Nat, +x: Nat, +h: {C.fits(a, x) == True{} : Bool}) -> {C.fits(Nat.add(a, d), x) == True{} : Bool}:
  +e = N.eq_from_is_eq(C.high(a, x), 0n, h)
  %Equal.sym(Nat, C.high(Nat.add(a, d), x), C.high(d, C.high(a, x)), WW.high_comp(d, a, x)) : {Nat.is_eq(_, 0n) == True{} : Bool}
  %Equal.sym(Nat, C.high(a, x), 0n, e) : {Nat.is_eq(C.high(d, _), 0n) == True{} : Bool}
  fits0(d)

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.sym
  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_eq
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=eq_from_is_eq
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/random/float.bend&name=fits0
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/width.bend&name=high_comp
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=fits
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=high