[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 29 from proof nouninit-addarrays (previous step)

newref_list(i→n(countrefs(ints)), st) = r ' + refs, 0 ≤ i, posints(ints), class ∈ claset, jvmref -- mkfs(class, void_type, `initstate' .field) ' ∈ addarrays(r ' + refs, ty, ints, i, st) ∧ (addarrays(r ' + refs, ty, ints, i, st)[jvmref -- mkfs(class, void_type, `initstate' .field) ']) = initval(undone) ∨ ¬ jvmref -- mkfs(class, void_type, `initstate' .field) ' ∈ addarrays(r ' + refs, ty, ints, i, st) ∧ _uninit ∈ addarrays(r ' + refs, ty, ints, i, st) ⊦ claset = ∅, ints = [], # claset = 0, jvmref = r, initundone(class, st), 1 + # refs = i→n(countrefs(ints)) ∧ ¬ jvmref ∈ refs

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 27:
⊦ # refs ≠ # refs0 → refs ≠ refs0
Proof step 28:
¬ # newref_list(i→n(countrefs(ints)), st) ≠ # (r ' + refs), newref_list(i→n(countrefs(ints)), st) = r ' + refs, 0 ≤ i, posints(ints), class ∈ claset, jvmref -- mkfs(class, void_type, `initstate' .field) ' ∈ addarrays(r ' + refs, ty, ints, i, st) ∧ (addarrays(r ' + refs, ty, ints, i, st)[jvmref -- mkfs(class, void_type, `initstate' .field) ']) = initval(undone) ∨ ¬ jvmref -- mkfs(class, void_type, `initstate' .field) ' ∈ addarrays(r ' + refs, ty, ints, i, st) ∧ _uninit ∈ addarrays(r ' + refs, ty, ints, i, st) ⊦ claset = ∅, ints = [], # claset = 0, jvmref = r, initundone(class, st), 1 + # refs = i→n(countrefs(ints)) ∧ ¬ jvmref ∈ refs

Rule argument

[speclemmaarg: ,# refs ≠ # refs0 → refs ≠ refs0 ,[refs0, refs] → [r ' + refs, newref_list(i→n(countrefs(ints)), st)] ,F ,list-data ,references ,length-neq ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (r ' + refs, newref_list(i→n(countrefs(ints)), st))]]