08eb78a5b2
This PR sets up the new integrated test/bench suite. It then migrates all benchmarks and some related tests to the new suite. There's also some documentation and some linting. For now, a lot of the old tests are left alone so this PR doesn't become even larger than it already is. Eventually, all tests should be migrated to the new suite though so there isn't a confusing mix of two systems.
72 lines
4.7 KiB
Text
72 lines
4.7 KiB
Text
[grind.debug.proof] Lean.Grind.intro_with_eq (x < y + z) (x + 1 ≤ y + z) (y + 1 < z → z + x < 3 * z)
|
|
(Lean.Grind.Nat.lt_eq x (y + z)) fun h =>
|
|
Lean.Grind.intro_with_eq (y + 1 < z) (y + 2 ≤ z) (z + x < 3 * z)
|
|
(Eq.trans (Lean.Grind.Nat.lt_eq (y + 1) z)
|
|
(id
|
|
(Nat.Linear.ExprCnstr.eq_of_toNormPoly_eq (Lean.RArray.branch 1 (Lean.RArray.leaf y) (Lean.RArray.leaf z))
|
|
{ eq := false, lhs := ((Nat.Linear.Expr.var 0).add (Nat.Linear.Expr.num 1)).add (Nat.Linear.Expr.num 1),
|
|
rhs := Nat.Linear.Expr.var 1 }
|
|
{ eq := false, lhs := (Nat.Linear.Expr.var 0).add (Nat.Linear.Expr.num 2), rhs := Nat.Linear.Expr.var 1 }
|
|
(eagerReduce (Eq.refl true)))))
|
|
fun h_1 =>
|
|
Classical.byContradiction
|
|
(Lean.Grind.intro_with_eq (¬z + x < 3 * z) (2 * z ≤ x) False
|
|
(Eq.trans
|
|
(congrArg Not
|
|
(Eq.trans (Lean.Grind.Nat.lt_eq (z + x) (3 * z))
|
|
(id
|
|
(Nat.Linear.ExprCnstr.eq_of_toNormPoly_eq
|
|
(Lean.RArray.branch 1 (Lean.RArray.leaf x) (Lean.RArray.leaf z))
|
|
{ eq := false,
|
|
lhs := ((Nat.Linear.Expr.var 1).add (Nat.Linear.Expr.var 0)).add (Nat.Linear.Expr.num 1),
|
|
rhs := Nat.Linear.Expr.mulL 3 (Nat.Linear.Expr.var 1) }
|
|
{ eq := false, lhs := (Nat.Linear.Expr.var 0).add (Nat.Linear.Expr.num 1),
|
|
rhs := Nat.Linear.Expr.mulL 2 (Nat.Linear.Expr.var 1) }
|
|
(eagerReduce (Eq.refl true))))))
|
|
(Eq.trans (Nat.not_le_eq (x + 1) (2 * z))
|
|
(id
|
|
(Nat.Linear.ExprCnstr.eq_of_toNormPoly_eq
|
|
(Lean.RArray.branch 1 (Lean.RArray.leaf x) (Lean.RArray.leaf z))
|
|
{ eq := false, lhs := (Nat.Linear.Expr.mulL 2 (Nat.Linear.Expr.var 1)).add (Nat.Linear.Expr.num 1),
|
|
rhs := (Nat.Linear.Expr.var 0).add (Nat.Linear.Expr.num 1) }
|
|
{ eq := false, lhs := Nat.Linear.Expr.mulL 2 (Nat.Linear.Expr.var 1), rhs := Nat.Linear.Expr.var 0 }
|
|
(eagerReduce (Eq.refl true))))))
|
|
fun h_2 =>
|
|
id
|
|
(let ctx :=
|
|
Lean.RArray.branch 1 (Lean.RArray.leaf ↑x)
|
|
(Lean.RArray.branch 2 (Lean.RArray.leaf ↑y) (Lean.RArray.leaf ↑z));
|
|
let p_1 := Poly.num 12;
|
|
let p_2 := Poly.add (-1) 2 (Poly.add 1 1 (Poly.num 2));
|
|
let p_3 := Poly.add (-1) 2 (Poly.add (-1) 1 (Poly.add 1 0 (Poly.num 1)));
|
|
let p_4 := Poly.add 2 1 (Poly.add (-1) 0 (Poly.num 4));
|
|
let p_5 := Poly.add 2 2 (Poly.add (-1) 0 (Poly.num 0));
|
|
let p_6 := Poly.add (-2) 1 (Poly.add 1 0 (Poly.num 2));
|
|
let e_1 := Expr.var 2;
|
|
let e_2 := Expr.var 0;
|
|
let e_3 := (Expr.var 1).add (Expr.var 2);
|
|
let e_4 := Expr.mulL 2 (Expr.var 2);
|
|
let e_5 := (Expr.var 1).add (Expr.num 2);
|
|
let e_6 := (Expr.var 0).add (Expr.num 1);
|
|
le_unsat ctx p_1 (eagerReduce (Eq.refl true))
|
|
(le_combine ctx p_6 p_4 p_1 (eagerReduce (Eq.refl true))
|
|
(le_combine ctx p_3 p_5 p_6 (eagerReduce (Eq.refl true))
|
|
(le_norm_expr ctx e_6 e_3 p_3 (eagerReduce (Eq.refl true))
|
|
(Nat.ToInt.of_le (Nat.ToInt.add_congr (Eq.refl ↑x) (Nat.ToInt.natCast_ofNat 1))
|
|
(Nat.ToInt.add_congr (Eq.refl ↑y) (Eq.refl ↑z)) h))
|
|
(le_norm_expr ctx e_4 e_2 p_5 (eagerReduce (Eq.refl true))
|
|
(Nat.ToInt.of_le (Nat.ToInt.mul_congr (Nat.ToInt.natCast_ofNat 2) (Eq.refl ↑z)) (Eq.refl ↑x)
|
|
h_2)))
|
|
(le_combine ctx p_2 p_5 p_4 (eagerReduce (Eq.refl true))
|
|
(le_norm_expr ctx e_5 e_1 p_2 (eagerReduce (Eq.refl true))
|
|
(Nat.ToInt.of_le (Nat.ToInt.add_congr (Eq.refl ↑y) (Nat.ToInt.natCast_ofNat 2)) (Eq.refl ↑z) h_1))
|
|
(le_norm_expr ctx e_4 e_2 p_5 (eagerReduce (Eq.refl true))
|
|
(Nat.ToInt.of_le (Nat.ToInt.mul_congr (Nat.ToInt.natCast_ofNat 2) (Eq.refl ↑z)) (Eq.refl ↑x)
|
|
h_2))))))
|
|
private theorem ex1 : ∀ (x y z : Nat), x < y + z → y + 1 < z → z + x < 3 * z :=
|
|
fun x y z => ex1._proof_1_1 x y z
|
|
private theorem ex2 : ∀ {p : Prop} (x y z : Nat), x < y + z → y + 1 < z → (p ↔ z + x < 3 * z) → p :=
|
|
fun {p} x y z => ex2._proof_1_1 x y z
|
|
private theorem ex3 : ∀ (x y : Nat),
|
|
27 ≤ 13 * x + 11 * y → 13 * x + 11 * y ≤ 30 → 7 * y ≤ 9 * x + 10 → 9 * x ≤ 4 + 7 * y → False :=
|
|
fun x y => ex3._proof_1_1 x y
|