lean4-htt/tests/lean/grind/algebra/exponents.lean
Leonardo de Moura 2713c846f1
chore: update tests/lean/grind todo folder (#9683)
Remove examples that we have already moved to `tests/lean/run`, and add
notes for possible fixes.
2025-08-02 13:10:34 +00:00

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Text

open Lean.Grind
section CommRing
variable (R : Type) [CommRing R]
example (a : R) (n m : Nat) : a^((n+m)^2) = a^(n^2 + 2*n*m + m^2) := by grind
example (a : R) (n m : Nat) : a^((n+m)^2) = a^(n^2) * a^(2*n*m) * a^(m^2) := by grind
-- from Mathlib.NumberTheory.Multiplicity
theorem pow_two_pow_sub_pow_two_pow.extracted_1_1 {x y : R} (d : Nat) :
x ^ 2 ^ (d + 1) - y ^ 2 ^ (d + 1) = (x ^ 2 ^ d + y ^ 2 ^ d) * (x ^ 2 ^ d - y ^ 2 ^ d) := by
grind
end CommRing
section Field
variable (F : Type) [Field F]
example (a : F) (n m : Int) : a^(n - m) = a^n / a^m := by grind
example (a : F) (n m : Int) : a^((n - m) * (n + m)) = a^(n^2) / a^(m^2) := by grind
end Field