cdaa827b2a
This PR fixes a bug in the `grind linarith` model/counterexample construction. Closes #10500
80 lines
2 KiB
Text
80 lines
2 KiB
Text
open Lean Grind Std
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set_option warn.sorry false
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namespace Ex1
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variable [Field Q] [LT Q] [LE Q] [LawfulOrderLT Q] [IsLinearOrder Q] [OrderedRing Q]
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variable (a₁ a₂ a₃ a₄ a₅ : Q)
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variable (α L ν : Q)
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/--
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trace: [grind.linarith.model] a₁ := 0
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[grind.linarith.model] a₂ := 0
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[grind.linarith.model] a₃ := 0
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[grind.linarith.model] a₄ := 0
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[grind.linarith.model] a₅ := 0
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[grind.linarith.model] α := 0
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[grind.linarith.model] L := 0
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[grind.linarith.model] ν := 2
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-/
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#guard_msgs in
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set_option trace.grind.linarith.model true in
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theorem upper_bound
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(hL : L = α) (hL1 : L ≤ 1)
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(ha₁ : 0 ≤ a₁) (ha₂ : 0 ≤ a₂) (ha₃ : 0 ≤ a₃) (ha₄ : 0 ≤ a₄) (ha₅ : 0 ≤ a₅)
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(hα : α = a₁ + a₂ + a₃ + a₄ + a₅) :
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ν ≤ 9/10 := by
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fail_if_success grind
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sorry
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end Ex1
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namespace Ex2
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variable (a₁ a₂ a₃ a₄ a₅ : Rat)
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variable (α L ν : Rat)
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/--
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trace: [grind.linarith.model] a₁ := 0
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[grind.linarith.model] a₂ := 0
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[grind.linarith.model] a₃ := 0
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[grind.linarith.model] a₄ := 0
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[grind.linarith.model] a₅ := 0
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[grind.linarith.model] α := 0
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[grind.linarith.model] L := 0
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[grind.linarith.model] ν := 2
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-/
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#guard_msgs in
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set_option trace.grind.linarith.model true in
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theorem upper_bound
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(hL : L = α) (hL1 : L ≤ 1)
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(ha₁ : 0 ≤ a₁) (ha₂ : 0 ≤ a₂) (ha₃ : 0 ≤ a₃) (ha₄ : 0 ≤ a₄) (ha₅ : 0 ≤ a₅)
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(hα : α = a₁ + a₂ + a₃ + a₄ + a₅) :
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ν ≤ 9/10 := by
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fail_if_success grind
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sorry
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end Ex2
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/--
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trace: [grind.linarith.model] a := 0
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[grind.linarith.model] b := 0
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[grind.linarith.model] c := 0
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-/
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#guard_msgs in
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set_option trace.grind.linarith.model true in
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example [Field α] [LE α] [LT α] [Std.IsPreorder α] [OrderedRing α] (a b c : α) (h : a = b + c) : False := by
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fail_if_success grind
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sorry
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/--
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trace: [grind.linarith.model] a := 0
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[grind.linarith.model] b := 0
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[grind.linarith.model] c := 0
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-/
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#guard_msgs in
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set_option trace.grind.linarith.model true in
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example (a b c : Rat) (h : a = b + c) : False := by
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fail_if_success grind
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sorry
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