| /- Copyright (c) Heather Macbeth, 2023. All rights reserved. -/ |
| import Library.Theory.ModEq.Lemmas |
| import Library.Tactic.Extra.Attr |
| import Mathlib.Tactic.Positivity |
|
|
| /- # `extra` tactic |
|
|
| A tactic which proves goals such as |
| `example (m n : ℝ) (hn : 10 ≤ n) : m + 68 * n ^ 2 ≥ m` |
|
|
| -/ |
|
|
| |
| set_option hygiene false in |
| / |
| macro (name := extra) "extra" : tactic => |
| `(tactic |
| | first |
| | focus (aesop (rule_sets [extra, -default]) (simp_options := { enabled := false }); done) |
| | fail "out of scope: extra proves relations between a LHS and a RHS differing by some neutral quantity for the relation") |
|
|
| lemma IneqExtra.neg_le_sub_self_of_nonneg [LinearOrderedAddCommGroup G] {a b : G} (h : 0 ≤ a) : |
| -b ≤ a - b := by |
| rw [sub_eq_add_neg] |
| apply le_add_of_nonneg_left h |
|
|
| attribute [aesop safe (rule_sets [extra]) apply] |
| le_add_of_nonneg_right le_add_of_nonneg_left |
| lt_add_of_pos_right lt_add_of_pos_left |
| IneqExtra.neg_le_sub_self_of_nonneg |
| add_le_add_left add_le_add_right add_lt_add_left add_lt_add_right |
| sub_le_sub_left sub_le_sub_right sub_lt_sub_left sub_lt_sub_right |
| le_refl |
|
|
| attribute [aesop safe (rule_sets [extra]) apply] |
| Int.modEq_fac_zero Int.modEq_fac_zero' Int.modEq_zero_fac Int.modEq_zero_fac' |
| Int.modEq_add_fac_self Int.modEq_add_fac_self' Int.modEq_add_fac_self'' Int.modEq_add_fac_self''' |
| Int.modEq_sub_fac_self Int.modEq_sub_fac_self' Int.modEq_sub_fac_self'' Int.modEq_sub_fac_self''' |
| Int.modEq_add_fac_self_symm Int.modEq_add_fac_self_symm' Int.modEq_add_fac_self_symm'' Int.modEq_add_fac_self_symm''' |
| Int.modEq_sub_fac_self_symm Int.modEq_sub_fac_self_symm' Int.modEq_sub_fac_self_symm'' Int.modEq_sub_fac_self_symm''' |
| Int.ModEq.add_right Int.ModEq.add_left |
| Int.ModEq.sub_right Int.ModEq.sub_left |
| Int.ModEq.refl |
|
|
| def extra.Positivity : Lean.Elab.Tactic.TacticM Unit := |
| Lean.Elab.Tactic.liftMetaTactic fun g => do Mathlib.Meta.Positivity.positivity g; pure [] |
|
|
| attribute [aesop safe (rule_sets [extra]) tactic] extra.Positivity |
|
|
