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Theorem at-mod

tree[p] = dnode(md0, sdt0) ⊦ tree.dir? ∧ p ∈ tree ∧ q ∈ tree[p, dnode(md1, sdt1)] → tree[p, dnode(md1, sdt1)][q] = (q ⊑ p ⊃ tree[q][restn(# q, p), dnode(md1, sdt1)];tree[p, dnode(md0, sdt1)][q])

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: 14
Proof steps: 31
Used lemmas: fnode-notin, at-dnode-same, one-at, one-ind, put-here, put-rec, split-at, split-in, at-dnode, in-dnode, nil-in, nil-put, nil-at, dnode-elim-strong,
Used spec theorems:
- directory-tree-base/At-other
- store/directory-tree-inst/exin
Used simplifier rules:
- directory-tree-base/dnode-inj
- list-last/path/prefix-nil
- nat-basic/c
- nat-basic/a
- list-del/path/weak-restN-rec
- nat-basic/succ
- list/path/len-05
- list/path/c
- list-last/path/prefix-empty
- list/path/e-01
- list-last/path/prefix-one-01
- list-del/path/restN-zero
- list-data/path/size-01
- list/path/app
- list/path/app-04
- list/path/c-03
- store/directory-tree-inst/insin
- list-last/path/prefix-rec-02
- directory-tree-base/At-same
- list-last/path/prefix-rec-03
- list/path/a
- directory-tree-base/In-insert
- directory-tree-base/At-other
- store/directory-tree-inst/in-neq