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Theorem in-del

p ≠ ε ⊦ p ∈ tree → (q ∈ tree -- p ↔ ¬ p ⊑ q ∧ q ∈ tree)

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 5
Proof steps: 15
Used lemmas: one-inf, fnode-notin, del-recin, del-here, in-dnode, nil-in, one-at, one-ind, split-in,
Used spec theorems:
- Used simplifier rules:
  - list-last/path/prefix-empty
  - list/path/e-01
  - list/path/c
  - list/path/app
  - directory-tree-base/Del-in
  - directory-tree-base/Del-at
  - list-last/path/prefix-one
  - directory-tree-base/At-other
  - directory-tree-base/In-insert
  - list-last/path/prefix-rec-03
  - list/path/a
  - directory-tree-base/At-same
  - list-last/path/prefix-rec-02
  - store/directory-tree-inst/insin