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Theorem inter-subset-rem-empty

⊦ ns0 ∩ ns1 = ∅ ∧ ns2 ⊆ ns1 → (ns0 \ ns3) ∩ ns2 = ∅

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 1
Proof steps: 3
Used lemmas:
Used spec theorems:
- set-basic/nat-set/Extension
Used simplifier rules:
- set-basic/nat-set/size-zero
- set-basic/nat-set/size-zero-01
- set-basic/nat-set/In-empty
- set-union/nat-set/Intersect
- set-union/nat-set/int-a
- set-union/nat-set/int-c
- set-union/nat-set/Difference
- set-basic/nat-set/ne-01
- set-basic/nat-set/sub-in
- set-union/nat-set/int-empty-02