lean4-htt/tests/lean/hpow.lean
Rob23oba 797985e319
feat: upstream several Rat lemmas from mathlib (#10077)
This PR upstreams lemmas about `Rat` from `Mathlib.Data.Rat.Defs` and
`Mathlib.Algebra.Order.Ring.Unbundled.Rat`, specifically enough to get
`Lean.Grind.Field Rat` and `Lean.Grind.OrderedRing Rat`. In addition to
the lemmas, instances for `Inv Rat`, `Pow Rat Nat` and `Pow Rat Int`
have been upstreamed.

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Co-authored-by: Kim Morrison <kim@tqft.net>
2025-08-25 06:02:27 +00:00

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/-!
Test the `rightact%` elaborator for `HPow.hPow`, added to address #2854
-/
open Lean
variable (n : Nat) (m : Int) (q : Rat)
#check n ^ 2 + m ^ 2
#check n ^ 2 + 1
#check (n ^ 2 + 1 : Int)
#check (n ^ 2 + (1 : Nat) : Int)
#check q ^ n + 1
#check q ^ m + 1
#check q ^ (n : Int) + 1
#check 12 * q + 1 ≤ 13 * q ^ 2
#check (12 : Rat) * q + (1 : Rat) ≤ (13 : Rat) * q ^ 2