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Proof step 5 from proof addarrays-length-01 (previous step)

1 + n→i(# refs) = countrefs(i ' + ints0), newref(r, st), is_newref_list(refs, st), posints(ints0), 0 ≤ i ⊦ r = jvmref, (addarrays(r ' + refs, ty, i ' + ints0, 0, st)[r -- _length]) = intval(i), r ∈ refs

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ posints(ints) ∧ ints ≠ [] ∧ 0 ≤ i ∧ n→i(# (r ' + refs)) = countrefs(ints) ∧ is_newref_list(r ' + refs, st) → (addarrays(r ' + refs, ty, ints, i, st)[r -- _length]) = intval(ints .first)
Proof step 4:
¬ (posints(i ' + ints0) ∧ i ' + ints0 ≠ [] ∧ 0 ≤ 0 ∧ n→i(# (r ' + refs)) = countrefs(i ' + ints0) ∧ is_newref_list(r ' + refs, st)), 1 + n→i(# refs) = countrefs(i ' + ints0), newref(r, st), is_newref_list(refs, st), posints(ints0), 0 ≤ i ⊦ r = jvmref, (addarrays(r ' + refs, ty, i ' + ints0, 0, st)[r -- _length]) = intval(i), r ∈ refs

Rule argument

[crewrite-arg: addarrays-length , F , [st, i, ints, ty, refs, r] → [st, 0, i ' + ints0, ty, refs, r] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ # (refs + refs0) = # refs + # refs0], [CSIMPSEQ : ⊦ # r ' = 0 +1], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ n→i(m + n) = n→i(m) + n→i(n)], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (i ' + ints) .first = i], [CSIMPSEQ : ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1], [CSIMPSEQ : ⊦ intval(i) = intval(i0) ↔ i = i0])], [EXTRATERMS : (st, 0, i ' + ints0, ty, refs, r)]]