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Theorem crash-exists-h

⊦ ∃ fs1. (∀ fid. fid ∈ fs1 ↔ fid ∈ tree.fids ∧ fid ∈ fs0) ∧ (∀ fid. fid ∈ fs1 → fs1[fid] = fs0[fid])

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 25
Proof steps: 45
Used lemmas:
Used spec theorems:
- directory-tree/tree-induction
- store/file-data-store/In-insert
- store/directory-tree-inst/exnotempty
- store+set/file-data-store/oplus-l-in
- bag-union/fidbag/in-union
- store+set/file-data-store/oplus-l-at-left
Used simplifier rules:
- directory-tree-fids/fids-dnode
- bag-union/fidbag/in-one
- directory-tree-fids/fids-fnode
- store/file-data-store/insin
- store/file-data-store/in-neq
- store/file-data-store/k-At-same
- store/file-data-store/In-empty
- bag-union/fidbag/in-emp
- directory-tree-fids/fids-emp
- directory-tree-base/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
- store+set/file-data-store/oplus-l-at-right
- store+set/file-data-store/oplus-l-in