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Theorem challenge3
r ≠ null, (tr(r, t) * P)(H), bst(t) ⊦ 〈search_tree_delete_min(; a, r, H)〉 ((tr(r, t .butleftmost) * P * true)(H) ∧ bst(t .butleftmost) ∧ a = t .leftmost ∧ ¬ a ∈ t .butleftmost ∧ (∀ b. b ∈ t .butleftmost → a < b))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 14
Proof steps: 34
Used lemmas:
ismin
,
leftmost-in
,
in-branch
,
in-leaf
,
bst-leaf
,
butleftmost-in
,
butleftmost-bst
,
bst-branch
,
leftmost
,
bst-branch-strong
,
butleftmost
,
program+leftmost
,
Used spec theorems:
Used simplifier rules:
oelem
/
sls
oelem
/
transitivity
oelem
/
irreflexivity
heap-sep
/node-heap/
prop
heap-sep
/node-heap/
and
heap-sep
/node-heap/
and-com
heap-sep
/node-heap/
and-ass
heap-sep
/node-heap/
emp-sep
heap-sep
/node-heap/
prop-shift
linked-tree
/
tr-base
heap-sep
/node-heap/
true-elim
heap-sep
/node-heap/
sep-com
heap-sep
/node-heap/
sep-ass
linked-tree
/
tr-unfold