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Theorem fids-exists

⊦ ∃ fids. ∀ fid. fid ∈ fids ↔ fid ∈ tree.fids

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 17
Proof steps: 29
Used lemmas:
Used spec theorems:
- directory-tree/tree-induction
- store/directory-tree-inst/exnotempty
- set-union/fidset/unrax
- bag-union/fidbag/in-union
Used simplifier rules:
- directory-tree-fids/fids-dnode
- bag-union/fidbag/in-one
- directory-tree-fids/fids-fnode
- set-union/fidset/One
- set-basic/fidset/in-04
- bag-union/fidbag/in-emp
- directory-tree-fids/fids-emp
- directory-tree-base/In-empty
- set-basic/fidset/In-empty
- directory-tree-fids/fids-ins
- directory-tree-base/At-same
- store/directory-tree-inst/insin
- directory-tree-base/Size-insert
- nat-basic/s-04
- nat-basic/ref
- nat-basic/a
- nat-basic/c
- directory-tree-base/In-insert
- store/directory-tree-inst/At-in-out