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Theorem in-put

tree[p] = dnode(md, sdt) ⊦ tree.dir? ∧ p ∈ tree → (q ∈ tree[p, dnode(md, sdt[str, tree0])] ↔ (p + str ' ⊑ q ⊃ restn(# p + 1, q) ∈ tree0;q ∈ tree))

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 7
Proof steps: 31
Used lemmas: fnode-notin, one-at, one-ind, put-here, put-rec, split-in, at-dnode, in-dnode, nil-in, nil-put, nil-at, dnode-elim-strong, one-restn,
Used spec theorems:
- store/directory-tree-inst/exin
Used simplifier rules:
- list/path/app-02
- directory-tree-base/dnode-inj
- nat-basic/succ
- list/path/len-05
- nat-basic/c
- nat-basic/a
- list/path/e-02
- list/path/c-03
- list-last/path/prefix-one-01
- list/path/c-07
- list-del/path/restN-zero
- list-data/path/size-01
- list/path/Nil
- list/path/app
- directory-tree-base/At-other
- list-last/path/prefix-rec-02
- store/directory-tree-inst/insin
- list/path/c
- list/path/e-01
- list-last/path/prefix-one
- store/directory-tree-inst/k-At-same
- directory-tree-base/In-insert
- list-last/path/prefix-empty
- list/path/e
- list-data/path/elim-list-c
- store/directory-tree-inst/insins
- directory-tree-base/At-same
- store/directory-tree-inst/in-neq
- store/directory-tree-inst/At-in-out
- list-last/path/prefix-rec-03
- list/path/a