2a67a49f31
This PR deprecates the tactics `simp_arith`, `simp_arith!`, `simp_all_arith` and `simp_all_arith!`. Users can just use the `+arith` option.
36 lines
1.4 KiB
Text
36 lines
1.4 KiB
Text
inductive TreeNode where
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| mkLeaf (name : String) : TreeNode
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| mkNode (name : String) (children : List TreeNode) : TreeNode
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def treeToList (t : TreeNode) : List String :=
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match t with
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| .mkLeaf name => [name]
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| .mkNode name children => Id.run do
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let mut r := [name]
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for h : child in children do
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-- We will not this the following `have` in the future
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have : sizeOf child < 1 + sizeOf name + sizeOf children := Nat.lt_trans (List.sizeOf_lt_of_mem h) (by simp +arith)
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r := r ++ treeToList child
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return r
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@[simp] theorem treeToList_eq (name : String) (children : List TreeNode) : treeToList (.mkNode name children) = name :: List.flatten (children.map treeToList) := by
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simp [treeToList, Id.run]
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mutual
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def numNames : TreeNode → Nat
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| .mkLeaf _ => 1
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| .mkNode _ cs => 1 + numNamesLst cs
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def numNamesLst : List TreeNode → Nat
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| [] => 0
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| a :: as => numNames a + numNamesLst as
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end
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theorem length_treeToList_eq_numNames (t : TreeNode) : (treeToList t).length = numNames t := by
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match t with
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| .mkLeaf .. => simp [treeToList, numNames]
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| .mkNode _ cs => simp +arith [numNames, helper cs]
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where
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helper (cs : List TreeNode) : (cs.map treeToList).flatten.length = numNamesLst cs := by
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match cs with
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| [] => simp [List.flatten, numNamesLst]
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| c::cs' => simp [List.flatten, List.map, numNamesLst, length_treeToList_eq_numNames c, helper cs']
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