| /- Copyright (c) Heather Macbeth, 2023. All rights reserved. -/ |
| import Mathlib.Algebra.GroupPower.Order |
| import Mathlib.Tactic.Positivity |
|
|
| open Lean |
|
|
| syntax (name := cancelDischarger) "cancel_discharger " : tactic |
| syntax (name := cancelAux) "cancel_aux " term " at " term : tactic |
| syntax (name := cancel) "cancel " term " at " term : tactic |
|
|
| macro_rules | `(tactic| cancel_discharger) => `(tactic | positivity) |
| macro_rules |
| | `(tactic| cancel_discharger) =>`(tactic | fail "cancel failed, could not verify the following side condition:") |
|
|
| /-! ### powers -/ |
| macro_rules |
| | `(tactic| cancel_aux $a at $h) => |
| let h := h.raw.getId |
| `(tactic | replace $(mkIdent h):ident := lt_of_pow_lt_pow (n := $a) (by cancel_discharger) $(mkIdent h)) |
| macro_rules |
| | `(tactic| cancel_aux $a at $h) => |
| let h := h.raw.getId |
| `(tactic | replace $(mkIdent h):ident := le_of_pow_le_pow (n := $a) (by cancel_discharger) (by cancel_discharger) $(mkIdent h)) |
| macro_rules |
| | `(tactic| cancel_aux $a at $h) => |
| let h := h.raw.getId |
| `(tactic | replace $(mkIdent h):ident := pow_eq_zero (n := $a) $(mkIdent h)) |
|
|
|
|
| /-! ### multiplication, LHS and RHS -/ |
| macro_rules |
| | `(tactic| cancel_aux $a at $h) => |
| let h := h.raw.getId |
| `(tactic | replace $(mkIdent h):ident := mul_left_cancel₀ (a := $a) (by cancel_discharger) $(mkIdent h)) |
| macro_rules |
| | `(tactic| cancel_aux $a at $h) => |
| let h := h.raw.getId |
| `(tactic | replace $(mkIdent h):ident := mul_right_cancel₀ (b := $a) (by cancel_discharger) $(mkIdent h)) |
| macro_rules |
| | `(tactic| cancel_aux $a at $h) => |
| let h := h.raw.getId |
| `(tactic | replace $(mkIdent h):ident := le_of_mul_le_mul_left (a := $a) $(mkIdent h) (by cancel_discharger)) |
| macro_rules |
| | `(tactic| cancel_aux $a at $h) => |
| let h := h.raw.getId |
| `(tactic | replace $(mkIdent h):ident := le_of_mul_le_mul_right (a := $a) $(mkIdent h) (by cancel_discharger)) |
| macro_rules |
| | `(tactic| cancel_aux $a at $h) => |
| let h := h.raw.getId |
| `(tactic | replace $(mkIdent h):ident := lt_of_mul_lt_mul_left (a := $a) $(mkIdent h) (by cancel_discharger)) |
| macro_rules |
| | `(tactic| cancel_aux $a at $h) => |
| let h := h.raw.getId |
| `(tactic | replace $(mkIdent h):ident := lt_of_mul_lt_mul_right (a := $a) $(mkIdent h) (by cancel_discharger)) |
|
|
| /-! ### multiplication, just LHS -/ |
| macro_rules |
| | `(tactic| cancel_aux $a at $h) => |
| let h := h.raw.getId |
| `(tactic | replace $(mkIdent h):ident := pos_of_mul_pos_right (a := $a) $(mkIdent h) (by cancel_discharger)) |
| macro_rules |
| | `(tactic| cancel_aux $a at $h) => |
| let h := h.raw.getId |
| `(tactic | replace $(mkIdent h):ident := pos_of_mul_pos_left (b := $a) $(mkIdent h) (by cancel_discharger)) |
| macro_rules |
| | `(tactic| cancel_aux $a at $h) => |
| let h := h.raw.getId |
| `(tactic | replace $(mkIdent h):ident := nonneg_of_mul_nonneg_right (a := $a) $(mkIdent h) (by cancel_discharger)) |
| macro_rules |
| | `(tactic| cancel_aux $a at $h) => |
| let h := h.raw.getId |
| `(tactic | replace $(mkIdent h):ident := nonneg_of_mul_nonneg_left (b := $a) $(mkIdent h) (by cancel_discharger)) |
|
|
| -- TODO to trigger this needs some `guard_hyp` in the `cancel_aux` implementations |
| elab_rules : tactic |
| | `(tactic| cancel $a at $h) => do |
| let goals ← Elab.Tactic.getGoals |
| let goalsMsg := MessageData.joinSep (goals.map MessageData.ofGoal) m!"\n\n" |
| throwError "cancel failed: no '{a}' to cancel\n{goalsMsg}" |
|
|
| -- TODO build in a `try change 1 ≤ _ at h` to upgrade the `0 < _` result in the case of Nat |
| macro_rules | `(tactic| cancel $a at $h) => `(tactic| cancel_aux $a at $h; try apply $h) |
|
|
