def below_difference

stelliferous@0.0.2.0 · proofs/nat_order.bend:357

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

357# Translate a comparison against a remaining extent to its absolute position.
358def below_difference(+offset: Nat,+value: Nat,+end: Nat,ordered: {Nat.is_le(offset,end) == True{} : Bool}) ->
359  {Nat.is_lt(value,Nat.sub(end,offset)) == Nat.is_lt(Nat.add(offset,value),end) : Bool}:
360  match offset end:
361    case 0n end:
362      %Equal.sym(Nat,Nat.sub(end,0n),end,subtract_zero(end)) : {Nat.is_lt(value,_) == Nat.is_lt(value,end) : Bool}
363      {==}
364    case 1n+offset 0n:
365      Empty.absurd({Nat.is_lt(value,Nat.sub(0n,1n+offset)) == Nat.is_lt(Nat.add(1n+offset,value),0n) : Bool},WordEncoding.false_true(ordered))
366    case 1n+offset 1n+end: below_difference(offset,value,end,ordered)