NatExtrema.below_minimum: def of stelliferous@0.0.2.0
Import: import stelliferous@0.0.2.0/proofs/nat_extrema.bend as NatExtrema
Lines 111-119 of stelliferous@0.0.2.0/proofs/nat_extrema.bend: https://jend.leeeet.dev/read.txt?path=stelliferous@0.0.2.0/proofs/nat_extrema.bend&start_line=111&end_line=119

import Base

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

Uses (6):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.and
  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_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.min
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/nat_extrema.bend&name=below_zero_right