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Theorem valid-group-nodes-entire

⊦ # gndx ≤ valid-group-nodes(gndx) ↔ valid-group-nodes(gndx) = # gndx

Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by: dom-remove-refsize0-down, down-store-notin-notin, in-nodes-down-at-same, nodes-crash-down, nodes-write-same-flushed, remove-refsize0-down,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 1
Proof steps: 1
Used lemmas: valid-group-nodes-ls, valid-group-nodes-rec, valid-group-nodes-base, induction-rev-list,
Used spec theorems:
- Used simplifier rules:
  - list-data/group-store/size-01
  - list/group-store/Last
  - list/group-store/len
  - list/group-store/len-02
  - list/group-store/a
  - nat/succ-01
  - nat-basic/a
  - nat-basic/c
  - list/group-store/in-15
  - nat-basic/eq-01
  - nat/lels-03
  - list/group-store/in-append
  - list/group-store/in-17
  - nat-basic/lf-02
  - nat-basic/f
  - oelem/nat-set/irreflexivity
  - nat-basic/s-04
  - nat/le-def
  - nat/lels
  - list-data/group-store/l
  - nat-basic/l-02
  - nat/let
  - nat-basic/eq-02