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Proof step 17 from proof getarray-addarray-03 (previous step)

0 ≤ i, ∀ st, val, r, i0. i→n(i0) < i→n(i) → (0 ≤ i0 → getarray(r, 0, i0, addarray(r, val, i0, st)) = mklist(val, i→n(i0))) ⊦ getarray(r, 0, i, addarray(r, val, i, st)) = mklist(val, i→n(i))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ i > 0 → addarray(r, val, i, st) = (addarray(r, val, i - 1, st)[r -- (i - 1) ', val])
Proof step 2:
⊦ addarray(r, val, 0, st) = st
Proof step 16:
i > 0, 0 ≤ i, ∀ st, val, r, i0. i→n(i0) < i→n(i) → (0 ≤ i0 → getarray(r, 0, i0, addarray(r, val, i0, st)) = mklist(val, i→n(i0))) ⊦ getarray(r, 0, i, addarray(r, val, i - 1, st)[r -- (i - 1) ', val]) = mklist(val, i→n(i))

Rule argument

[crewrite-arg: addarray-rec, F, [st, i, val, r] → [st, i, val, r]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i > j ↔ j < i], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i ≤ j → (j ≤ i ↔ i = j)], [CSIMPSEQ : ⊦ getarray(r, i, 0, st) = []], [CSIMPSEQ : ⊦ mklist(val, 0) = []])], [EXTRATERMS : (st, i, val, r)]]