975b6e758f
This PR improves the counterexamples produced by `grind linarith` for `NatModule`s. `grind` now hides occurrences of the auxiliary function `Grind.IntModule.OfNatModule.toQ`.
68 lines
1.8 KiB
Text
68 lines
1.8 KiB
Text
open Lean Grind Std
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variable (M : Type) [NatModule M]
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section
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variable [AddRightCancel M]
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example (x y : M) : 2 • x + 3 • y + x = 3 • (x + y) := by
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grind
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end
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section
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variable [LE M] [LT M] [LawfulOrderLT M] [IsLinearOrder M] [OrderedAdd M]
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example {x y : M} (h : x ≤ y) : 2 • x + y ≤ 3 • y := by
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grind
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end
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section
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variable [LE M] [LT M] [LawfulOrderLT M] [IsPreorder M] [OrderedAdd M]
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example {x y : M} : x ≤ y → 2 • x + y > 3 • y → False := by
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grind
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example {x y z : M} : x ≤ y → y < z → 2 • x + y ≥ 3 • z → False := by
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grind
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end
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section
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variable [LE M] [IsLinearOrder M] [OrderedAdd M] [AddRightCancel M]
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example {x y : M} : x + x ≤ y → y ≤ 2 • x → x + x ≠ y → False := by
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grind
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end
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section
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variable [AddRightCancel M]
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example {x y : M} : x + x = y → 2•x ≠ y → False := by
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grind
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example {x y z : M} : x + z = y → x = z → 2•x ≠ y → False := by
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grind
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example {x y z : M} : x + z = y → x = 2•z → 3•z ≠ y → False := by
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grind
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end
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section
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variable [LE M] [IsLinearOrder M] [OrderedAdd M] [AddRightCancel M]
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example {x y z : M} : x + z = y → x = 2•z → 3•z ≠ y → False := by
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grind
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end
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example [NatModule α] [AddRightCancel α] [LE α] [LT α] [LawfulOrderLT α] [IsLinearOrder α] [OrderedAdd α] (a b c d : α)
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: a ≤ b → a ≥ c + d → d ≤ 0 → d ≥ 0 → b = c → a = b := by
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grind
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/--
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trace: [grind.linarith.model] a := 0
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[grind.linarith.model] b := 1
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[grind.linarith.model] c := 1
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[grind.linarith.model] d := -2
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-/
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#guard_msgs (drop error, trace) in
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set_option trace.grind.linarith.model true in
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example [NatModule α] [AddRightCancel α] [LE α] [LT α] [LawfulOrderLT α] [IsLinearOrder α] [OrderedAdd α] (a b c d : α)
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: a ≤ b → a ≥ c + d → b = c → a = b := by
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grind
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