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Theorem rem-stays-reachable-aux

reachable(r, r0, h), h[r0].nxt ≠ null, h[r0].nxt ∈ h, h[r0].nxt ≠ h[h[r0].nxt].nxt, ce.nxt = h[h[r0].nxt].nxt ⊦ reachable(r, h[r0].nxt, h[r0 := ce]) ↔ h[h[r0].nxt].nxt = h[r0].nxt ∨ r ≠ r0 ∧ r = h[r0].nxt ∨ (∃ x. path(r ' + x + h[r0].nxt ', h) ∧ r0 ≠ r ∧ ¬ r0 ∈ x) ∨ (∃ x. path(h[r0].nxt ' + x + h[r0].nxt ', h) ∧ ¬ r0 ∈ x)

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 39
Proof steps: 74
Used lemmas: path-last-not-null, path-trans, path-first-in-H, reachable-def, path-postfix, path-prefix, path-modify-strong, path-two, path-modify, path-cons, path-one, reachable-nodups-def, reach-alloc,
Used spec theorems:
Used simplifier rules:
- list/a
- list-dup/rec
- list-last/last-one
- list/app
- list/in-empty
- list-dup/e-01
- store/insin
- list/in-06
- list/c
- store/At-same
- list-last/last-rec
- list-last/last-elim
- list/in-17
- list/in-append
- list-dup/f
- list/e-02
- list/in-01
- list/in-rec
- list-dup/f-01
- list/Nil
- store/in-neq
- list-last/last-01
- list/Last
- store/k-At-same
- store/At-other