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Proof step 132 from proof addarray-put-01 (previous step)

0 ≤ i0, i ≤ i0, 0 < i, 0 < i0 ⊦ (addarray(r, ty, 1 + i0, st)[r -- i ']) = (val ' + mklist(initial_value(ty), i→n(i0)))[i→n(i)], i = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 117:
⊦ n < # vals → (vals + vals0)[n] = vals[n]
Proof step 131:
¬ i→n(i) < # val ', 0 ≤ i0, i ≤ i0, 0 < i, 0 < i0 ⊦ (addarray(r, ty, 1 + i0, st)[r -- i ']) = (val ' + mklist(initial_value(ty), i→n(i0)))[i→n(i)], i = 0

Rule argument

[speclemmaarg: ,n < # vals → (vals + vals0)[n] = vals[n] ,[n, vals0, vals] → [i→n(i), mklist(initial_value(ty), i→n(i0)), val '] ,F ,list-del ,javavalues ,get-append-less ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ # val ' = 0 +1], [CSIMPSEQ : ⊦ i ≠ j → (i ≤ j ↔ i < j)], [CSIMPSEQ : 0 ≤ i ⊦ i→n(i) < ((* m)) ↔ i < n→i(m)], [CSIMPSEQ : ⊦ i < 1 ↔ i ≤ 0], [CSIMPSEQ : ⊦ i < j → ¬ j < i])], [EXTRATERMS : (i→n(i), mklist(initial_value(ty), i→n(i0)), val ')]]