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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
- map/insin
- list/in-06
- list/c
- map/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
- map/in-neq
- list-last/last-01
- list/Last
- map/k-At-same
- map/At-other