62fa92ec4a
This PR implements support for positive constraints in `grind order`.
The new module can already solve problems such as:
```lean
example [LE α] [LT α] [Std.LawfulOrderLT α] [Std.IsPreorder α]
(a b c : α) : a ≤ b → b ≤ c → c < a → False := by
grind
example [LE α] [LT α] [Std.LawfulOrderLT α] [Std.IsPreorder α]
(a b c d : α) : a ≤ b → b ≤ c → c < d → d ≤ a → False := by
grind
example [LE α] [Std.IsPreorder α]
(a b c : α) : a ≤ b → b ≤ c → a ≤ c := by
grind
example [LE α] [Std.IsPreorder α]
(a b c d : α) : a ≤ b → b ≤ c → c ≤ d → a ≤ d := by
grind
```
It also generalizes support for offset constraints in `grind` to rings.
The new module implements theory propagation and reduces the number of
case splits required to solve problems:
```lean
example [LE α] [LT α] [Std.LawfulOrderLT α] [Std.IsPreorder α] [Ring α] [OrderedRing α]
(a b : α) : a ≤ 5 → b ≤ 8 → a > 6 ∨ b > 10 → False := by
grind -linarith (splits := 0)
example [LE α] [LT α] [Std.LawfulOrderLT α] [Std.IsPreorder α] [CommRing α] [OrderedRing α]
(a b c : α) : a + b*c + 2*c ≤ 5 → a + c > 5 - c - c*b → False := by
grind -linarith (splits := 0)
example (a b : Int) (h : a + b > 5) : (if a + b ≤ 0 then b else a) = a := by
grind -linarith -cutsat (splits := 0)
```
We still need to implement support for negated constraints.
51 lines
2.1 KiB
Text
51 lines
2.1 KiB
Text
open Lean Grind
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example [LE α] [LT α] [Std.LawfulOrderLT α] [Std.IsPreorder α]
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(a b c : α) : a ≤ b → b ≤ c → c < a → False := by
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grind
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example [LE α] [LT α] [Std.LawfulOrderLT α] [Std.IsPreorder α]
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(a b c d : α) : a ≤ b → b ≤ c → c < d → d ≤ a → False := by
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grind
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example [LE α] [Std.IsPreorder α]
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(a b c : α) : a ≤ b → b ≤ c → a ≤ c := by
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grind
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example [LE α] [Std.IsPreorder α]
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(a b c d : α) : a ≤ b → b ≤ c → c ≤ d → a ≤ d := by
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grind
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example [LE α] [LT α] [Std.LawfulOrderLT α] [Std.IsPreorder α] [Ring α] [OrderedRing α]
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(a b c : α) : a ≤ b → b ≤ c → c < a → False := by
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grind -linarith
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example [LE α] [LT α] [Std.LawfulOrderLT α] [Std.IsPreorder α] [Ring α] [OrderedRing α]
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(a b : α) : a ≤ 5 → b ≤ 8 → a > 6 ∨ b > 10 → False := 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 : α) : a + b*c + 2*c ≤ 5 → a + c > 5 - c - c*b → False := by
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grind -linarith (splits := 0)
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example [LE α] [LT α] [Std.LawfulOrderLT α] [Std.IsPreorder α] [Ring α] [OrderedRing α]
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(a b c : α) : a - b ≤ 5 → -c + b ≤ -3 → c < a - 2 → False := by
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grind -linarith
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example [LE α] [LT α] [Std.LawfulOrderLT α] [Std.IsPreorder α] [Ring α] [OrderedRing α]
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(a b c : α) : a - b ≤ 5 → -c + b < -3 → c < a - 2 → False := by
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grind -linarith
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example [LE α] [LT α] [Std.LawfulOrderLT α] [Std.IsPreorder α] [Ring α] [OrderedRing α]
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(a b c : α) : a - b < 5 → -c + b < -3 → c < a - 2 → False := by
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grind -linarith
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example [LE α] [LT α] [Std.LawfulOrderLT α] [Std.IsPreorder α] [Ring α] [OrderedRing α]
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(a b c : α) : a - b < 5 → -c + b ≤ -3 → c < a - 2 → False := by
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grind -linarith
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example (a b c : Int) : a - b ≤ 5 → -c + b ≤ -3 → c < a - 2 → False := by
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grind -linarith -cutsat
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example (a b : Int) (h : a + b > 5) : (if a + b ≤ 0 then b else a) = a := by
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grind -linarith -cutsat (splits := 0)
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