Nat.min_add_add_left_sym: law of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/nat.bend as Nat
Lines 4648-4653 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=4648&end_line=4653

import Base

# A common left summand leaves the minimum: min (a + b) (a + c) = a + min b c, reversed to rewrite toward the simple side.
law min_add_add_left_sym:
  for a: Nat
  for -b: Nat
  for -c: Nat
  {Nat.add(a, Nat.min(b, c)) == Nat.min(Nat.add(a, b), Nat.add(a, c)) : Nat}

Uses (5):
  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.add
  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=min_add_add_left