NatOrder.ge_false: def of stelliferous@0.0.2.0
Import: import stelliferous@0.0.2.0/proofs/nat_order.bend as NatOrder
Lines 240-249 of stelliferous@0.0.2.0/proofs/nat_order.bend: https://jend.leeeet.dev/read.txt?path=stelliferous@0.0.2.0/proofs/nat_order.bend&start_line=240&end_line=249

import Base
import stelliferous@0.0.2.0/proofs/word_encoding.bend as WordEncoding

def ge_false(+a: Nat,+b: Nat,h: {Nat.is_ge(a,b) == False{} : Bool}) -> {Nat.is_lt(a,b) == True{} : Bool}:
  match a b:
    case 0n 0n:
      Empty.absurd({Nat.is_lt(0n,0n) == True{} : Bool},WordEncoding.false_true(Equal.sym(Bool,True{},False{},h)))
    case 0n 1n+b:
      {==}
    case 1n+a 0n:
      Empty.absurd({Nat.is_lt(1n+a,0n) == True{} : Bool},WordEncoding.false_true(Equal.sym(Bool,True{},False{},h)))
    case 1n+a 1n+b:
      ge_false(a,b,h)

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=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.is_ge
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/word_encoding.bend&name=false_true