40e1e097c1
This PR fixes a nontermination and missing propagation bug in `grind order`. It also register relevant case-splits for arithmetic. Closes #11001
106 lines
2.3 KiB
Text
106 lines
2.3 KiB
Text
/-!
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Test propagation rules for `grind order`
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-/
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example (p q : Prop) : ((0 : Rat) < (1 : Rat) → p)
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→ ¬ p ∨ q
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→ ¬ p ∨ ¬q
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→ False
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:= by
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grind -linarith (splits := 0)
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example (p q : Prop) : ((0 : Rat) ≤ (1 : Rat) → p)
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→ ¬ p ∨ q
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→ ¬ p ∨ ¬q
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→ False
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:= by
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grind -linarith (splits := 0)
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example (p q s : Prop) : (if (0 : Rat) < (1 : Rat) then p else s)
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→ ¬ p ∨ q
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→ ¬ p ∨ ¬q
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→ False
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:= by
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grind -linarith (splits := 0)
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example (p q s : Prop) : (if (0 : Rat) ≤ (0 : Rat) then p else s)
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→ ¬ p ∨ q
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→ ¬ p ∨ ¬q
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→ False
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:= by
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grind -linarith (splits := 0)
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example (p q s : Prop) : (if (0 : Rat) > (1 : Rat) then s else p)
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→ ¬ p ∨ q
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→ ¬ p ∨ ¬q
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→ False
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:= by
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grind -linarith (splits := 0)
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example (p q s : Prop) : (if (0 : Rat) >= (1 : Rat) then s else p)
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→ ¬ p ∨ q
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→ ¬ p ∨ ¬q
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→ False
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:= by
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grind -linarith (splits := 0)
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-----
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example (p q : Prop) (a : Rat) : (a < a + 1 → p)
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→ ¬ p ∨ q
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→ ¬ p ∨ ¬q
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→ False
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:= by
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grind -linarith (splits := 0)
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example (p q : Prop) (a : Rat) : (a ≤ a → p)
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→ ¬ p ∨ q
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→ ¬ p ∨ ¬q
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→ False
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:= by
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grind -linarith (splits := 0)
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example (p q s : Prop) (a : Rat) : (if a < a + 1 then p else s)
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→ ¬ p ∨ q
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→ ¬ p ∨ ¬q
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→ False
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:= by
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grind -linarith (splits := 0)
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example (p q s : Prop) (a : Rat) : (if a ≤ a then p else s)
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→ ¬ p ∨ q
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→ ¬ p ∨ ¬q
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→ False
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:= by
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grind -linarith (splits := 0)
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example (p q s : Prop) (a : Rat) : (if a > a + 1 then s else p)
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→ ¬ p ∨ q
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→ ¬ p ∨ ¬q
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→ False
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:= by
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grind -linarith (splits := 0)
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example (p q s : Prop) (a : Rat) : (if a >= a + 1 then s else p)
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→ ¬ p ∨ q
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→ ¬ p ∨ ¬q
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→ False
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:= by
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grind -linarith (splits := 0)
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-----
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example [LE α] [Std.IsPreorder α] [DecidableLE α] (a : α) (p q s : Prop)
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: (if a ≤ a then p else s)
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→ ¬ p ∨ q
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→ ¬ p ∨ ¬q
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→ False
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:= by
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grind (splits := 0)
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example [LE α] [LT α] [Std.LawfulOrderLT α] [Std.IsPreorder α] [DecidableLT α] (a : α) (p q s : Prop)
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: (if a < a then s else p)
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→ ¬ p ∨ q
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→ ¬ p ∨ ¬q
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→ False
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:= by
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grind (splits := 0)
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