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Theorem FOWs-FO-split

⊦ bel.FOWs(t, l) = fowl0 + FO(t) ' + fowl1 ↔ (∃ bel0, bel1. bel = bel0 + FO(l) ' + bel1 ∧ fowl0 = bel0.FOWs(t, l) ∧ fowl1 = bel1.FOWs(t, l))

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 11
Proof steps: 34
Used lemmas: FOWs-one-FO, FOWs-W, FOWs-one-W, FOWs-SF, FOWs-one-SF, FOWs-base, FOWs-FO, FOWs-append,
Used spec theorems:
- Used simplifier rules:
  - list/a
  - list/len-01
  - list/app-02
  - list/e
  - list/c
  - list/Nil
  - FOW/disj-FO-W
  - list/inapp-02
  - list/in-rec
  - list/in-append
  - list/in-14
  - list/c-06