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Theorem elems-subseteq-add-diff-notin
⊦ ¬ n ∈ nx0 ∧ elems nx1 ⊆ elems nx0 → (elems nx0 ++ n) \ elems nx1 = (elems nx0 \ elems nx1) ++ n
Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
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the proof
Infos about the proof
Proved?: Yes
Interactions: 4
Proof steps: 9
Used lemmas:
elems-in-fwd
,
elems-in-diff
,
elems-def
,
Used spec theorems:
set-basic
/nat-set/
Extension
set-union
/nat-set/
Difference
Used simplifier rules:
set-basic
/nat-set/
In-insert
set-basic
/nat-set/
in-02