1d971c8735
This PR implements the Rabinowitsch transformation for `Field` disequalities in `grind`. For example, this transformation is necessary for solving: ```lean example [Field α] (a : α) : a^2 = 0 → a = 0 := by grind ```
38 lines
774 B
Text
38 lines
774 B
Text
variable (d : Nat) in
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inductive X : Nat → Prop
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| f {s : Nat} : X s
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| g {s : Nat} : X d → X s
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/--
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error: `grind` failed
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case grind.1
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c : Nat
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q : X c 0
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s : Nat
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h : 0 = s
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h_1 : ⋯ ≍ ⋯
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⊢ False
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[grind] Goal diagnostics
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[facts] Asserted facts
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[prop] X c 0
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[prop] 0 = s
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[prop] ⋯ ≍ ⋯
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[eqc] True propositions
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[prop] X c 0
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[prop] X c s
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[eqc] Equivalence classes
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[eqc] {0, s}
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[cases] Case analyses
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[cases] [1/2]: X c 0
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[cases] source: Initial goal
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[cutsat] Assignment satisfying linear constraints
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[assign] c := 2
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[assign] s := 0
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-/
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#guard_msgs (error) in
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example {c : Nat} (q : X c 0) : False := by
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grind -mbtc [cases X]
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example {c : Nat} (q : X c 0) : False := by
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fail_if_success grind [cases X]
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sorry
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