PROOFText.wsd.kn: def of bend-osdev-word64@0.1.1.0
Import: import bend-osdev-word64@0.1.1.0/PROOF_text.bend as PROOFText
Lines 135-138 of bend-osdev-word64@0.1.1.0/PROOF_text.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-word64@0.1.1.0/PROOF_text.bend&start_line=135&end_line=138

import Base
import bend-osdev-u32@0.1.0.0/u32.bend as U
import bend-osdev-u32@0.1.0.0/LAWS.bend as UL
import bend-osdev-u32@0.1.0.0/LAWS_order.bend as UO

# x < 2^h 10: x < 2^n (for 10 <= 2^h)
def wsd.kn(+n: Nat, +h: Nat, +x: Nat, +en: {Nat.add(h, h) == n : Nat}, +h10: {Nat.is_le(10n, U.U32Nat.dbl(h, 1n)) == True{} : Bool}, +hx: {Nat.is_lt(x, U.U32Nat.dbl(h, 10n)) == True{} : Bool}) -> {Nat.is_lt(x, U.U32Nat.dbl(n, 1n)) == True{} : Bool}:
  +hh = UO.nat_lt_le_trans(x, U.U32Nat.dbl(h, 10n), U.U32Nat.dbl(h, U.U32Nat.dbl(h, 1n)), hx, Equal.trans(Bool, Nat.is_le(U.U32Nat.dbl(h, 10n), U.U32Nat.dbl(h, U.U32Nat.dbl(h, 1n))), Nat.is_le(10n, U.U32Nat.dbl(h, 1n)), True{}, UL.dbl_le(h, 10n, U.U32Nat.dbl(h, 1n)), h10))
  Equal.trans(Bool, Nat.is_lt(x, U.U32Nat.dbl(n, 1n)), Nat.is_lt(x, U.U32Nat.dbl(h, U.U32Nat.dbl(h, 1n))), True{}, Equal.cong(Nat, Bool, zz => Nat.is_lt(x, zz), U.U32Nat.dbl(n, 1n), U.U32Nat.dbl(h, U.U32Nat.dbl(h, 1n)), Equal.sym(Nat, U.U32Nat.dbl(h, U.U32Nat.dbl(h, 1n)), U.U32Nat.dbl(n, 1n), Equal.sym(Nat, U.U32Nat.dbl(n, 1n), U.U32Nat.dbl(h, U.U32Nat.dbl(h, 1n)), wm.fn(h, n, 1n, en)))), hh)

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.is_lt
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=dbl_le
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS_order.bend&name=nat_lt_le_trans
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/u32.bend&name=U32Nat.dbl
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/PROOF_text.bend&name=wm.fn