def below_minimum

stelliferous@0.0.2.0 · proofs/nat_extrema.bend:111

import Base

111# A lane belongs to a clipped count exactly when it belongs to both bounds.
112def below_minimum(+value: Nat,+left: Nat,+right: Nat) ->
113  {Nat.is_lt(value,Nat.min(left,right)) == Nat.is_lt(value,left) && Nat.is_lt(value,right) : Bool}:
114  match value left right:
115    case value 0n right: {==}
116    case value 1n+left 0n:
117      below_zero_right(Nat.is_lt(value,1n+left))
118    case 0n 1n+left 1n+right: {==}
119    case 1n+value 1n+left 1n+right: below_minimum(value,left,right)