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Theorem tree-ext

⊦ tree0 = tree1 ↔ (∀ p. (p ∈ tree0 ↔ p ∈ tree1) ∧ (p ∈ tree0 → (tree0[p].dir? ↔ tree1[p].dir?) ∧ (tree0[p].dir? ⊃ tree0[p].meta = tree1[p].meta;tree0[p].fid = tree1[p].fid)))

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: 11
Proof steps: 22
Used lemmas: at-dnode, in-dnode, one-at, one-ind, meta, isdnode, fnode-elim-strong, fid, isfnode, nil-at, nil-in, fnode-notin, tree-induction,
Used spec theorems:
- store/directory-tree-inst/k-Extension
Used simplifier rules:
- directory-tree-base/fnode-inj
- directory-tree-base/dnode-inj
- directory-tree-inst/read-notin
- list/path/c
- list/path/a
- directory-tree-base/disj