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Theorem prepost-get-min
bin-heap-inv(bh, ar), keyset(bh) ≠ ∅ ⊦ ⟪bin_min_heap_get_min#(bh; n)⟫ ∃ key. key-index(key, n) ∈ keyset(bh) ∧ (∀ ki. ki ∈ keyset(bh) → ¬ ki.key < key)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
prepost-extract-min
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 5
Proof steps: 22
Used lemmas:
bin-heap-inv-def
,
keyset
,
Used spec theorems:
bin-min-heap-inv
/
key-set-extract-index
bin-min-heap-inv
/
heap-order-min
Used simplifier rules:
bin-min-heap
/
elim
set-basic
/keyindex-set/
size-zero-01
set-basic
/keyindex-set/
size-zero
bin-min-heap
/
sel-01
bin-min-heap-inv
/
2exp-size-0
bin-min-heap
/
sel-02
key-index
/
elim
bin-min-heap-inv
/
keyset-base
set-basic
/keyindex-set/
Size-empty
nat
/
fle
nat-basic
/
f
key-index
/
sel-02
nat-basic
/
lf-02
nat-basic
/
zero
key-index
/
inj
oelem
/binheap-key/
lel
oelem
/binheap-key/
irreflexivity