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Theorem keyset-subarray-eq
m ≤ # kar0, m ≤ # kar1 ⊦ subarray(kar0, 0, m) = subarray(kar1, 0, m) → keyset(kar0, m) = keyset(kar1, m)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
keyset-subarray-eq-add
,
Used by units in proved state:
bin-min-heap-prepost
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 10
Proof steps: 20
Used lemmas:
keyset-rec
,
keyset-base
,
Used spec theorems:
array
/key-index-array/
Extension
array-copy
/key-index-array/
subarray-at
Used simplifier rules:
nat
/
succ-01
nat
/
lels-03
nat-basic
/
succ
nat-basic
/
trans
nat-basic
/
lf
nat-basic
/
f
nat-basic
/
eq-01
array-copy
/key-index-array/
size-subarray
nat-basic
/
ls-02
nat-basic
/
add-base
nat-basic
/
a
nat-basic
/
c
array-copy
/key-index-array/
subarray-at
nat-basic
/
s-04
nat-basic
/
ref
array-copy
/key-index-array/
subarray-elim