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Theorem inter-subseteq-simp

⊦ as0 ∩ as ⊆ as1 ∩ as ↔ as0 ∩ as ⊆ as1

Type: A user defined theorem
Validity: The proof is valid.
Features: ss, lss,
Comment:
Used by: inter-subseteq-weaken,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 2
Proof steps: 6
Used lemmas: subseteq-inter-same,
Used spec theorems:
- set-union/node-store/subdef
Used simplifier rules:
- set-union/node-store/int-subs01
- set-basic/node-store/sub-ntrans
- set-basic/node-store/size-zero-01
- set-basic/node-store/ne-01
- set-union/node-store/Intersect
- set-union/node-store/int-a
- set-union/node-store/int-c