f2e191d0af
This PR adds an explicit normalization layer for ring constraints in the `grind linarith` module. For example, it will be used to clean up denominators when the ring is a field.
37 lines
2.1 KiB
Text
37 lines
2.1 KiB
Text
module
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/--
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trace: [grind.debug.proof] fun h h_1 h_2 h_3 h_4 h_5 h_6 h_7 h_8 =>
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id
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(let ctx := RArray.branch 1 (RArray.leaf One.one) (RArray.leaf (f 2));
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let p_1 := Poly.nil;
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let p_2 := Poly.add 1 1 Poly.nil;
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let p_3 := Poly.add 1 0 Poly.nil;
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let p_4 := Poly.add (-1) 1 (Poly.add 1 0 Poly.nil);
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let p_5 := Poly.add (-1) 0 Poly.nil;
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let e_1 := (Expr.intMul 1 (Expr.var 1)).add (Expr.intMul 0 (Expr.var 0));
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let e_2 := Expr.zero;
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let e_3 := (Expr.intMul (-1) (Expr.var 1)).add (Expr.intMul 1 (Expr.var 0));
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let rctx := RArray.leaf (f 2);
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let rp_1 := CommRing.Poly.add 1 (CommRing.Mon.mult { x := 0, k := 1 } CommRing.Mon.unit) (CommRing.Poly.num 0);
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let rp_2 :=
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CommRing.Poly.add (-1) (CommRing.Mon.mult { x := 0, k := 1 } CommRing.Mon.unit) (CommRing.Poly.num 1);
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let re_1 := CommRing.Expr.var 0;
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let re_2 := CommRing.Expr.num 0;
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let re_3 := ((CommRing.Expr.num 1).neg.mul (CommRing.Expr.var 0)).add (CommRing.Expr.num 1);
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lt_unsat ctx
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(le_lt_combine ctx p_3 p_5 p_1 (eagerReduce (Eq.refl true))
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(le_le_combine ctx p_4 p_2 p_3 (eagerReduce (Eq.refl true))
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(le_norm ctx e_3 e_2 p_4 (eagerReduce (Eq.refl true))
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(CommRing.le_int_module rctx rp_2
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(CommRing.le_norm rctx re_3 re_2 rp_2 (eagerReduce (Eq.refl true)) h_8)))
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(le_norm ctx e_1 e_2 p_2 (eagerReduce (Eq.refl true))
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(CommRing.le_int_module rctx rp_1
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(CommRing.le_norm rctx re_1 re_2 rp_1 (eagerReduce (Eq.refl true)) h_1))))
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(zero_lt_one ctx p_5 (eagerReduce (Eq.refl true)) (Eq.refl One.one))))
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-/
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#guard_msgs in
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open Std Lean Grind Linarith in
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set_option trace.grind.debug.proof true in -- Context should contain only `f 2` and `One`
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example [CommRing α] [LE α] [LT α] [LawfulOrderLT α] [IsLinearOrder α] [OrderedRing α] (f : Nat → α) :
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f 1 <= 0 → f 2 <= 0 → f 3 <= 0 → f 4 <= 0 → f 5 <= 0 → f 6 <= 0 → f 7 <= 0 → f 8 <= 0 → -1 * f 2 + 1 <= 0 → False := by
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grind -order
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