def upper_bound_cases

stelliferous@0.0.2.0 · proofs/nat_order.bend:91

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

91def upper_bound_cases(+value: Nat,+limit: Nat,bounded: {Nat.is_le(value,limit) == True{} : Bool}) -> UpperBound<value,limit>:
92  match value limit:
93    case 0n 0n: At{{==}}
94    case 0n 1n+rest: Before{{==}}
95    case 1n+rest 0n: Empty.absurd(UpperBound<1n+rest,0n>,WordEncoding.false_true(bounded))
96    case 1n+ +previous 1n+ +last: lift_upper_bound(previous,last,upper_bound_cases(previous,last,bounded))