32 lines
1.7 KiB
Text
32 lines
1.7 KiB
Text
module
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/--
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trace: [grind.debug.proof] fun h h_1 h_2 h_3 =>
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Classical.byContradiction fun h_4 =>
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id
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(let ctx := RArray.branch 1 (RArray.leaf x) (RArray.leaf x⁻¹);
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let e_1 := (Expr.var 0).mul (Expr.var 1);
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let e_2 := Expr.num 0;
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let e_3 := Expr.num 1;
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let e_4 := (Expr.var 0).pow 2;
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let m_1 := Mon.mult (Power.mk 1 1) Mon.unit;
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let m_2 := Mon.mult (Power.mk 0 1) Mon.unit;
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let p_1 := Poly.num (-1);
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let p_2 := Poly.add (-1) (Mon.mult (Power.mk 0 1) Mon.unit) (Poly.num 0);
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let p_3 := Poly.add 1 (Mon.mult (Power.mk 0 2) Mon.unit) (Poly.num 0);
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let p_4 := Poly.add 1 (Mon.mult (Power.mk 0 1) (Mon.mult (Power.mk 1 1) Mon.unit)) (Poly.num (-1));
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let p_5 := Poly.add 1 (Mon.mult (Power.mk 0 1) Mon.unit) (Poly.num 0);
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one_eq_zero_unsat ctx p_1 (eagerReduce (Eq.refl true))
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(Stepwise.simp ctx 1 p_4 (-1) m_1 p_5 p_1 (eagerReduce (Eq.refl true))
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(Stepwise.core ctx e_1 e_3 p_4 (eagerReduce (Eq.refl true)) (diseq0_to_eq x h_4))
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(Stepwise.mul ctx p_2 (-1) p_5 (eagerReduce (Eq.refl true))
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(Stepwise.superpose ctx 1 m_2 p_4 (-1) m_1 p_3 p_2 (eagerReduce (Eq.refl true))
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(Stepwise.core ctx e_1 e_3 p_4 (eagerReduce (Eq.refl true)) (diseq0_to_eq x h_4))
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(Stepwise.core ctx e_4 e_2 p_3 (eagerReduce (Eq.refl true)) h)))))
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-/
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#guard_msgs in -- Context should contains only `x` and its inverse.
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set_option trace.grind.debug.proof true in
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set_option pp.structureInstances false in
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open Lean Grind CommRing in
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example [Field α] (x y z w : α) :
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x^2 = 0 → y^2 = 0 → z^3 = 0 → w^2 = 0 → x = 0 := by
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grind
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