Nat.lt_min_iff_sym: law of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/nat.bend as Nat
Lines 4698-4703 of bend-mathlib@0.8.1.0/nat.bend: https://jend.leeeet.dev/read.txt?path=bend-mathlib@0.8.1.0/nat.bend&start_line=4698&end_line=4703

import Base

# A number is below the minimum exactly when it is below both: a < min b c tests as a < b and a < c, reversed to rewrite toward the simple side.
law lt_min_iff_sym:
  for a: Nat
  for b: Nat
  for c: Nat
  {Bool.and(Nat.is_lt(a, b), Nat.is_lt(a, c)) == Nat.is_lt(a, Nat.min(b, c)) : Bool}

Uses (7):
  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=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_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.min
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=lt_min_iff