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Theorem In-insert
⊦ a ∈ s ++ b ↔ a = b ∨ a ∈ s
Type: An axiom
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by:
add
,
add-01
,
addthree
,
addtwo
,
del
,
eq
,
eq-01
,
eq-02
,
eq-04
,
eqtwo
,
eqtwo-01
,
ext-rec
,
in-02
,
in-05
,
indef
,
ins-two
,
ne
,
size-exgr
,
size-one
,
size-one-02
,
size-three
,
size-three-01
,
size-three-02
,
size-two
,
size-two-03
,
size-two-05
,
size-two-06
,
sizesubl
,
sub-add
,
sub-add-01
,
sub-add-02
,
sub-add-03
,
sub-add-04
,
sub-insert
,
sub-insert-3
,
sub-insert-4
,
sub-insert-5
,
subset
,
subset-ins
,
subset-insert
,
subset-insert-01
,
subset-insert-02
,
subset-insert-03
,
subset-insert-04
,
subset-insert-05
,
subset-insert-06
,
subset-insert-same
,
subsize-eq
,
sw-01
,
two
,
Used by units in proved state:
set-union
,
ostore+set
,
ostore
,
oset
,
natset
,
matrixops
,
Proof exists?: No