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Theorem Intersect
⊦ a ∈ s1 ∩ s2 ↔ a ∈ s1 ∧ a ∈ s2
Type: An axiom
Validity: The proof is valid.
Features: ws, ls,
Comment:
Used by:
add-inter-rem
,
diff-int
,
diff-int-01
,
empty-intersection-diff
,
int-a
,
int-c
,
int-del-rew
,
int-e
,
int-empty
,
int-empty-01
,
int-empty-02
,
int-eq
,
int-idem
,
int-ins
,
int-inse
,
int-inserte
,
int-notempty
,
int-notempty-01
,
int-subs01
,
intdel-empty
,
inter-empty-diff
,
intersect-add-rem
,
intersect-empty-rem
,
intersection-insert
,
intersection-shift
,
intexin
,
intu-empty
,
k-intersect-rec1
,
k-intersect-rec2
,
rem-inter-empty3
,
sub-rem-inter-rem
,
subset-is-union
,
subseteq-inter-empty-empty
,
union-inter-inter-union
,
union-sub-rem-inter-empty
,
Used by units in proved state:
Proof exists?: No