5306a3469d
This PR fixes a bug in the propagation rules for `ite` and `dite` used
in `grind`. The bug prevented equalities from being propagated to the
satellite solvers. Here is an example affected by this issue.
```lean
example
[LE α] [LT α] [Std.IsLinearOrder α] [Std.LawfulOrderLT α]
[Lean.Grind.CommRing α] [DecidableLE α] [Lean.Grind.OrderedRing α]
(a b c : α) :
(if a - b ≤ -(a - b) then -(a - b) else a - b) ≤
((if a - c ≤ -(a - c) then -(a - c) else a - c) + if c - d ≤ -(c - d) then -(c - d) else c - d) +
if b - d ≤ -(b - d) then -(b - d) else b - d := by
grind
```
75 lines
3.2 KiB
Text
75 lines
3.2 KiB
Text
/-
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The `ite` and `dite` propagators in `grind` were not internalizing
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their children using the correct parent information. Several examples
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in this file were failing because of this bug.
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-/
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example {α : Type _} [LE α] [LT α] [Std.IsLinearOrder α] [Std.LawfulOrderLT α]
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[Lean.Grind.IntModule α] [DecidableLE α] [Lean.Grind.OrderedAdd α]
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(a b c d : α)
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(h : ¬(-(a - b)) ≤ ((-(a - c)) + -(c - d)) + -(b - d))
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(h_1 : b - d ≤ -(b - d)) : False := by
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grind
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example {α : Type _} [LE α] [LT α] [Std.IsLinearOrder α] [Std.LawfulOrderLT α]
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[Lean.Grind.IntModule α] [DecidableLE α] [Lean.Grind.OrderedAdd α]
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(a b c d : α)
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(h : ¬(-(a - b)) ≤ ((-(a - c)) + -(c - d)) + if b - d ≤ -(b - d) then -(b - d) else b - d)
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(h_1 : b - d ≤ -(b - d)) : False := by
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grind
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example {α : Type _} [LE α] [LT α] [Std.IsLinearOrder α] [Std.LawfulOrderLT α]
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[Lean.Grind.CommRing α] [DecidableLE α] [Lean.Grind.OrderedRing α]
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(a b c : α)
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(h : a ≤ a + if b ≤ c then (-1 : α) else (-2))
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(h_1 : b ≤ c)
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: False := by
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grind
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example {α : Type _} [LE α] [LT α] [Std.IsLinearOrder α] [Std.LawfulOrderLT α]
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[Lean.Grind.CommRing α] [DecidableLE α] [Lean.Grind.OrderedRing α]
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(a b c : α)
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(h : a ≤ a + if b ≤ c then (-1 : α) else (-2))
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: False := by
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grind
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example [LE α] [LT α] [Std.IsLinearOrder α] [Std.LawfulOrderLT α] [Lean.Grind.CommRing α] [DecidableLE α] [Lean.Grind.OrderedRing α] (a b c : α) :
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(if a - b ≤ -(a - b) then -(a - b) else a - b) ≤
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((if a - c ≤ -(a - c) then -(a - c) else a - c) + if c - d ≤ -(c - d) then -(c - d) else c - d) +
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if b - d ≤ -(b - d) then -(b - d) else b - d := by
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grind
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example {α : Type _} [LE α] [LT α] [Std.IsLinearOrder α] [Std.LawfulOrderLT α]
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[Lean.Grind.IntModule α] [DecidableLE α] [Lean.Grind.OrderedAdd α]
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(a b c d : α)
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(h : ¬(-(a - b)) ≤ ((-(a - c)) + -(c - d)) + -(b - d))
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(h_1 : b - d ≤ -(b - d)) : False := by
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grind -order
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example {α : Type _} [LE α] [LT α] [Std.IsLinearOrder α] [Std.LawfulOrderLT α]
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[Lean.Grind.IntModule α] [DecidableLE α] [Lean.Grind.OrderedAdd α]
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(a b c d : α)
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(h : ¬(-(a - b)) ≤ ((-(a - c)) + -(c - d)) + if b - d ≤ -(b - d) then -(b - d) else b - d)
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(h_1 : b - d ≤ -(b - d)) : False := by
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grind -order
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example {α : Type _} [LE α] [LT α] [Std.IsLinearOrder α] [Std.LawfulOrderLT α]
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[Lean.Grind.CommRing α] [DecidableLE α] [Lean.Grind.OrderedRing α]
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(a b c : α)
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(h : a ≤ a + if b ≤ c then (-1 : α) else (-2))
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(h_1 : b ≤ c)
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: False := by
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grind -order
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example {α : Type _} [LE α] [LT α] [Std.IsLinearOrder α] [Std.LawfulOrderLT α]
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[Lean.Grind.CommRing α] [DecidableLE α] [Lean.Grind.OrderedRing α]
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(a b c : α)
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(h : a ≤ a + if b ≤ c then (-1 : α) else (-2))
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: False := by
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grind -order
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example [LE α] [LT α] [Std.IsLinearOrder α] [Std.LawfulOrderLT α] [Lean.Grind.CommRing α] [DecidableLE α] [Lean.Grind.OrderedRing α] (a b c : α) :
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(if a - b ≤ -(a - b) then -(a - b) else a - b) ≤
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((if a - c ≤ -(a - c) then -(a - c) else a - c) + if c - d ≤ -(c - d) then -(c - d) else c - d) +
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if b - d ≤ -(b - d) then -(b - d) else b - d := by
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grind -order
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