ProofValue.wn.add_lt_mono: def of bend-osdev-word64@0.1.1.0
Import: import bend-osdev-word64@0.1.1.0/proof_value.bend as ProofValue
Lines 183-187 of bend-osdev-word64@0.1.1.0/proof_value.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-word64@0.1.1.0/proof_value.bend&start_line=183&end_line=187

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

# a < b and c < d: a + c < b + d
def wn.add_lt_mono(+a: Nat, +b: Nat, +c: Nat, +d: Nat, h1: {Nat.is_lt(a, b) == True{} : Bool}, h2: {Nat.is_lt(c, d) == True{} : Bool}) -> {Nat.is_lt(Nat.add(a, c), Nat.add(b, d)) == True{} : Bool}:
  +s1 = Equal.trans(Bool, Nat.is_lt(Nat.add(a, c), Nat.add(b, c)), Nat.is_lt(a, b), True{}, wn.lt_add_r(a, b, c), h1)
  +s2 = Equal.trans(Bool, Nat.is_le(Nat.add(b, c), Nat.add(b, d)), Nat.is_le(c, d), True{}, wn.le_add_l(b, c, d), wn.lt_le(c, d, h2))
  UO.nat_lt_le_trans(Nat.add(a, c), Nat.add(b, c), Nat.add(b, d), s1, s2)

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.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_order.bend&name=nat_lt_le_trans
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/proof_value.bend&name=wn.le_add_l
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/proof_value.bend&name=wn.lt_add_r
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/proof_value.bend&name=wn.lt_le