3ce5097c3c
This PR implements the method `processNewEq` in `grind order`. It is responsible for processing equalities propagated by the `grind` E-graph.
58 lines
2.2 KiB
Text
58 lines
2.2 KiB
Text
open Lean Grind
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example [LE α] [LT α] [Std.LawfulOrderLT α] [Std.IsLinearPreorder α]
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(a b c d : α) : a ≤ b → ¬ (c ≤ b) → ¬ (d ≤ c) → d < a → False := by
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grind -linarith (splits := 0)
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example [LE α] [Std.IsLinearPreorder α]
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(a b c d : α) : a ≤ b → ¬ (c ≤ b) → ¬ (d ≤ c) → ¬ (a ≤ d) → False := by
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grind -linarith (splits := 0)
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example [LE α] [LT α] [Std.LawfulOrderLT α] [Std.IsLinearPreorder α] [CommRing α] [OrderedRing α]
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(a b c d : α) : a - b ≤ 5 → ¬ (c ≤ b) → ¬ (d ≤ c + 2) → d ≤ a - 8 → False := by
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grind -linarith (splits := 0)
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example [LE α] [LT α] [Std.LawfulOrderLT α] [Std.IsLinearPreorder α] [CommRing α] [OrderedRing α]
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(a b c d : α) : a - b ≤ 5 → ¬ (c < b) → ¬ (d ≤ c + 2) → d ≤ a - 8 → False := by
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grind -linarith (splits := 0)
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example (p : Prop) (a b c : Int) : (p ↔ b ≤ a) → (p ↔ c ≤ b) → ¬ p → c ≤ a + 1 → False := by
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grind -linarith -cutsat (splits := 0)
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/--
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error: `grind` failed
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case grind
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α : Type u_1
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inst : LE α
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inst_1 : Std.IsPreorder α
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a b c : α
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h : a ≤ b
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h_1 : b ≤ c
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h_2 : c ≤ a
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h_3 : ¬a = c
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⊢ False
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-/
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#guard_msgs in
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example [LE α] [Std.IsPreorder α]
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(a b c : α) : a ≤ b → b ≤ c → c ≤ a → a = c := by
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grind -linarith -verbose
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example [LE α] [Std.IsPartialOrder α]
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(a b c : α) : a ≤ b → b ≤ c → c ≤ a → a = c := by
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grind -linarith -verbose
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example [LE α] [Std.IsLinearPreorder α]
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(a b c d e : α) : a ≤ b → b = c → d = c → d ≤ e → a ≤ e := by
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grind -linarith (splits := 0)
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example [LE α] [Std.IsLinearPreorder α]
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(a b c d e : α) : a ≥ b → d = c → c = b → d ≥ e → a ≥ e := by
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grind -linarith (splits := 0)
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example [LE α] [LT α] [Std.LawfulOrderLT α] [Std.IsPreorder α] [CommRing α] [OrderedRing α]
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(a b c d e : α) : a ≥ b → d = c → c = b → d ≥ e → a ≥ e := by
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grind -linarith (splits := 0)
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example [LE α] [LT α] [Std.LawfulOrderLT α] [Std.IsPreorder α] [CommRing α] [OrderedRing α]
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(a b c d e : α) : a + 2 ≥ b → d = c → c = b → d + 1 ≥ e → a + 3 ≥ e := by
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grind -linarith (splits := 0)
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