NatExtrema.minimum_lower: def of stelliferous@0.0.2.0
Import: import stelliferous@0.0.2.0/proofs/nat_extrema.bend as NatExtrema
Lines 85-88 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=85&end_line=88

import Base

def minimum_lower(+left: Nat,+right: Nat,+lower: Nat,left_ok: {Nat.is_le(lower,left) == True{} : Bool},right_ok: {Nat.is_le(lower,right) == True{} : Bool}) ->
  {Nat.is_le(lower,Nat.min(left,right)) == True{} : Bool}:
  %Equal.sym(Nat,Nat.min(left,right),Bool.pick(Nat,Nat.is_lt(left,right),left,right),minimum_choice(left,right)) : {Nat.is_le(lower,_) == True{} : Bool}
  pick_lower(Nat.is_lt(left,right),left,right,lower,left_ok,right_ok)

Uses (9):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.pick
  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_le
  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=minimum_choice
  https://jend.leeeet.dev/definition.txt?path=stelliferous@0.0.2.0/proofs/nat_extrema.bend&name=pick_lower