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d03762b | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 | /- 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`
-/
-- See https://leanprover.zulipchat.com/#narrow/stream/270676-lean4/topic/hygiene.20question.3F/near/313556764
set_option hygiene false in
/-- A thin wrapper for `aesop`, which adds the `extra` rule set. -/
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
|