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Theorem ll-trav1-next

r1 ≠ null ⊦ (ll-trav(r0, r1, x) * P)(H) ∧ H[r1] = a × r → (¬ (ll-trav(r0, r, x) * P)(H) ↔ false)

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 3
Proof steps: 8
Used lemmas: lls-unfold-tail, lls-rec, lls-base, ll-trav1-def,
Used spec theorems:
- Used simplifier rules:
  - cell/inj
  - maplet/cell-heap/at-eq
  - maplet/cell-heap/ex1-shift
  - list/e-01
  - list/c
  - heap-sep/cell-heap/false-rev
  - heap-sep/cell-heap/false-and
  - heap-sep/cell-heap/and-ass
  - heap-sep/cell-heap/and-com
  - heap-sep/cell-heap/false-sep
  - heap-sep/cell-heap/falseH
  - list-data/elim-list-c
  - list/a
  - list/app-01
  - list/Last
  - heap-sep/cell-heap/sep-com
  - heap-sep/cell-heap/sep-ass