Nat.pow_lt_pow_left: law of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/nat.bend as Nat
Lines 3389-3395 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=3389&end_line=3395

import Base

# Positive powers are strictly monotone in the base: a < b implies a^(1 + n) < b^(1 + n).
law pow_lt_pow_left:
  for a: Nat
  for b: Nat
  for h: lt(a, b)
  for n: Nat
  lt(Nat.pow(a, 1n+n), Nat.pow(b, 1n+n))

Uses (7):
  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.mul
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.pow
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=lt
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=mul_lt_mul_of_lt_of_lt
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=mul_one