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Proof step 10 from proof getarray-put-03 (previous step)

0 < i0, ∀ j0, r, i, st, r0, fs, val. i→n(j0) < i→n(i0 + 1) → (true → getarray(r, i, j0, st[r0 -- fs ', val]) = getarray(r, i, j0, st)) ⊦ getarray(r, i, i0, st[r0 -- fs ', val]) + st[r -- (i + i0) '] ' = getarray(r, i, i0 + 1, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ 1 < j → getarray(r, i, j, st) = getarray(r, i, j - 1, st) + st[r -- (i + j - 1) ']
Proof step 9:
1 < i0 + 1, 0 < i0, ∀ j0, r, i, st, r0, fs, val. i→n(j0) < i→n(i0 + 1) → (true → getarray(r, i, j0, st[r0 -- fs ', val]) = getarray(r, i, j0, st)) ⊦ getarray(r, i, i0, st[r0 -- fs ', val]) + st[r -- (i + i0) '] ' = getarray(r, i, i0 + 1 - 1, st) + st[r -- (i + i0 + 1 - 1) ']

Rule argument

[crewrite-arg: getArray-rec, F, [st, j, i, r] → [st, i0 + 1, i, r]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ((* j)) < i0 + ((* j0)) ↔ j - j0 < i0], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i])], [EXTRATERMS : (st, i0 + 1, i, r)]]