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Proof step 12 from proof addarray-mklist-03 (previous step)

0 ≤ n→i(m) + n→i(m0), ∀ r, val, m, st. addarray(r, mklist(val, m0), n→i(m), addarray(r, mklist(val, m), 0, st)) = addarray(r, val, n→i(m0) + n→i(m), st) ⊦ addarray(r, mklist(val, m0 + 1), n→i(m), addarray(r, mklist(val, m), 0, st)) = (addarray(r, val, n→i(m0) + n→i(m), st)[r -- (n→i(m0) + n→i(m)) ', val])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ n ≠ 0 → mklist(val, n) = mklist(val, n -1) + val '
Proof step 11:
m0 + 1 ≠ 0, 0 ≤ n→i(m) + n→i(m0), ∀ r, val, m, st. addarray(r, mklist(val, m0), n→i(m), addarray(r, mklist(val, m), 0, st)) = addarray(r, val, n→i(m0) + n→i(m), st) ⊦ addarray(r, mklist(val, (m0 + 1) -1) + val ', n→i(m), addarray(r, mklist(val, m), 0, st)) = (addarray(r, val, n→i(m0) + n→i(m), st)[r -- (n→i(m0) + n→i(m)) ', val])

Rule argument

[speclemmaarg: ,n ≠ 0 → mklist(val, n) = mklist(val, n -1) + val ' ,[n, val] → [m0 + 1, val] ,F ,list-last ,javavalues ,mk-last-02 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m + 1 ≠ 0], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m])], [EXTRATERMS : (m0 + 1, val)]]