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Step * 1 of Lemma member-bs_tree_delete


1. [E] : Type
2. cmp : comparison(E)
3. x : E
⊢ bs_tree_ordered(E;cmp;bst_null())
⇒ (∀z:E. (z ∈ bs_tree_delete(cmp;x;bst_null()) ⇐⇒ z ∈ bst_null() ∧ (¬((cmp z x) = 0 ∈ ℤ))))
BY
{ (RepUR ``bs_tree_delete member_bs_tree`` 0 THEN Auto) }

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Latex:

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Latex:

1.  [E]  :  Type
2.  cmp  :  comparison(E)
3.  x  :  E
\mvdash{}  bs\_tree\_ordered(E;cmp;bst\_null())
{}\mRightarrow{}  (\mforall{}z:E.  (z  \mmember{}  bs\_tree\_delete(cmp;x;bst\_null())  \mLeftarrow{}{}\mRightarrow{}  z  \mmember{}  bst\_null()  \mwedge{}  (\mneg{}((cmp  z  x)  =  0))))


By

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Latex:
(RepUR  ``bs\_tree\_delete  member\_bs\_tree``  0  THEN  Auto)

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