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Theorem elems-in-diff

⊦ n ∈ nx0 ∧ ¬ n ∈ nx1 → n ∈ elems nx0 \ elems nx1

Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by: elems-subseteq-add-diff-notin,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 1
Proof steps: 3
Used lemmas: elems-def,
Used spec theorems:
- set-union/nat-set/Difference
Used simplifier rules: