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-rw-r--r--backends/lean/Base/Arith/Int.lean15
1 files changed, 13 insertions, 2 deletions
diff --git a/backends/lean/Base/Arith/Int.lean b/backends/lean/Base/Arith/Int.lean
index 3359ecdb..a57f8bb1 100644
--- a/backends/lean/Base/Arith/Int.lean
+++ b/backends/lean/Base/Arith/Int.lean
@@ -162,7 +162,7 @@ def introInstances (declToUnfold : Name) (lookup : Expr → MetaM (Option Expr))
-- Add a declaration
let nval ← Utils.addDeclTac name e type (asLet := false)
-- Simplify to unfold the declaration to unfold (i.e., the projector)
- Utils.simpAt [declToUnfold] [] [] (Tactic.Location.targets #[mkIdent name] false)
+ Utils.simpAt true [declToUnfold] [] [] (Location.targets #[mkIdent name] false)
-- Return the new value
pure nval
@@ -240,7 +240,7 @@ def intTac (splitGoalConjs : Bool) (extraPreprocess : Tactic.TacticM Unit) : Ta
-- the goal. I think before leads to a smaller proof term?
Tactic.allGoals (intTacPreprocess extraPreprocess)
-- More preprocessing
- Tactic.allGoals (Utils.tryTac (Utils.simpAt [] [``nat_zero_eq_int_zero] [] .wildcard))
+ Tactic.allGoals (Utils.tryTac (Utils.simpAt true [] [``nat_zero_eq_int_zero] [] .wildcard))
-- Split the conjunctions in the goal
if splitGoalConjs then Tactic.allGoals (Utils.repeatTac Utils.splitConjTarget)
-- Call linarith
@@ -270,6 +270,17 @@ elab "int_tac" args:(" split_goal"?): tactic =>
let split := args.raw.getArgs.size > 0
intTac split (do pure ())
+-- For termination proofs
+syntax "int_decr_tac" : tactic
+macro_rules
+ | `(tactic| int_decr_tac) =>
+ `(tactic|
+ simp_wf;
+ -- TODO: don't use a macro (namespace problems)
+ (first | apply Arith.to_int_to_nat_lt
+ | apply Arith.to_int_sub_to_nat_lt) <;>
+ simp_all <;> int_tac)
+
example (x : Int) (h0: 0 ≤ x) (h1: x ≠ 0) : 0 < x := by
int_tac_preprocess
linarith