ProofTab.gt.lt_sum: def of bend-osdev-gf@0.1.1.0
Import: import bend-osdev-gf@0.1.1.0/proof_tab.bend as ProofTab
Lines 156-164 of bend-osdev-gf@0.1.1.0/proof_tab.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-gf@0.1.1.0/proof_tab.bend&start_line=156&end_line=164

import Base

# a < m and b < n, so a + b < m + n
def gt.lt_sum(+a: Nat, +m: Nat, +b: Nat, +n: Nat, ha: {Nat.is_lt(a, m) == True{} : Bool}, +hb: {Nat.is_lt(b, n) == True{} : Bool}) -> {Nat.is_lt(Nat.add(a, b), Nat.add(m, n)) == True{} : Bool}:
  match a m:
    case 0n _:
      gt.lt_add_left(m, b, n, hb)
    case 1n+p 0n:
      Empty.absurd({Nat.is_lt(Nat.add(1n+p, b), n) == True{} : Bool}, gt.ft(ha))
    case 1n+p 1n+q:
      gt.lt_sum(p, q, b, n, ha, hb)

Uses (7):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  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_lt
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/proof_tab.bend&name=gt.ft
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-gf@0.1.1.0/proof_tab.bend&name=gt.lt_add_left