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Proof step 13 from proof multi-newrefs (previous step)

# refs = i→n(countrefs(i ' + ints0)), list2set(refs) ∩ list2set(refs0) = ∅, i ≤ i0, 0 ≤ i, posints(ints0), 0 ≤ i0 ⊦ (∀ r. r ∈ refs0 → newref(r, addmultiarrays(refs, i, acc, ty, i0 ' + ints0, st))) ↔ (∀ r. r ∈ refs0 → newref(r, st)), 0 ∈ (i0 ' + ints0) .butlast, dups(refs0)

User applied rule case distinction

And obtained the following new goals

Proof step 7:
∀ r. r ∈ refs0 → newref(r, addmultiarrays(refs, i, acc, ty, i0 ' + ints0, st)), # refs = i→n(countrefs(i ' + ints0)), list2set(refs) ∩ list2set(refs0) = ∅, i ≤ i0, 0 ≤ i, posints(ints0), 0 ≤ i0 ⊦ ∀ r. r ∈ refs0 → newref(r, st), 0 ∈ (i0 ' + ints0) .butlast, dups(refs0)
Proof step 12:
∀ r. r ∈ refs0 → newref(r, st), # refs = i→n(countrefs(i ' + ints0)), list2set(refs) ∩ list2set(refs0) = ∅, i ≤ i0, 0 ≤ i, posints(ints0), 0 ≤ i0 ⊦ ∀ r. r ∈ refs0 → newref(r, addmultiarrays(refs, i, acc, ty, i0 ' + ints0, st)), 0 ∈ (i0 ' + ints0) .butlast, dups(refs0)

Rule argument

[CASEDARG : pos: right 1, ()]

Additional information

[[CONCRETESIMPRULES : ()]]