U64int.fk: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/typed/u64int.bend as U64int
Lines 761-763 of bend-collections-laws-math@1.0.0.0/proofs/math/typed/u64int.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/u64int.bend&start_line=761&end_line=763

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/logic.bend as L
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/width.bend as WW

def fk(+K: Nat, +hK: {K == 64n : Nat}, +x: Nat, +h: {C.fits(64n, x) == True{} : Bool}) -> {Nat.is_lt(x, C.pow2(K)) == True{} : Bool}:
  +h2 = L.subst(Nat, z => {C.fits(z, x) == True{} : Bool}, 64n, K, Equal.sym(Nat, K, 64n, hK), h)
  Equal.trans(Bool, Nat.is_lt(x, C.pow2(K)), C.fits(K, x), True{}, Equal.sym(Bool, C.fits(K, x), Nat.is_lt(x, C.pow2(K)), WW.fits_lt(K, x)), h2)

Uses (9):
  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=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_lt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend&name=subst
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/width.bend&name=fits_lt
  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=pow2