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Proof step 7 from proof at-1dim-other-index-01 (previous step)

0 ≤ i0, i < 0 ∨ i0 < i, ∀ st, val, r, i, j0. i→n(j0) < i→n(i0 + 1) → (i < 0 ∨ j0 ≤ i → (addarray(r, val, j0, st)[r -- i ']) = st[r -- i ']) ⊦ (addarray(r, val, i0, st)[r -- i0 ', val][r -- i ']) = st[r -- i '], i = i0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ rk ≠ rk0 → (st[rk0, val][rk]) = st[rk]
Proof step 6:
r -- i ' ≠ r -- i0 ', 0 ≤ i0, i < 0 ∨ i0 < i, ∀ st, val, r, i, j0. i→n(j0) < i→n(i0 + 1) → (i < 0 ∨ j0 ≤ i → (addarray(r, val, j0, st)[r -- i ']) = st[r -- i ']) ⊦ (addarray(r, val, i0, st)[r -- i ']) = st[r -- i '], i = i0

Rule argument

[speclemmaarg: ,rk ≠ rk0 → (st[rk0, val][rk]) = st[rk] ,[rk, val, rk0, st] → [r -- i ', val, r -- i0 ', addarray(r, val, i0, st)] ,F ,store ,javastore ,At-other ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPSEQ : ⊦ i ' = i0 ' ↔ i = i0])], [EXTRATERMS : (r -- i ', val, r -- i0 ', addarray(r, val, i0, st))]]