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Proof step 3 from proof getarray-addarray-other-01 (previous step)

⊦ r = r0, getarray(r, i, j, addarray(r0, ty, vals, st)) = getarray(r, i, j, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ getarray(r, i, j, st) = getarray(r0, i0, j, st0) ↔ (∀ j0. 0 ≤ j0 ∧ j0 < j → st[r -- (i + j0) '] = st0[r0 -- (i0 + j0) '])
Proof step 2:
⊦ r ≠ r0 → (addarray(r, ty, vals, st)[r0 -- sk]) = st[r0 -- sk]

Rule argument

[speclemmaarg: , getarray(r, i, j, st) = getarray(r0, i0, j, st0) ↔ (∀ j0. 0 ≤ j0 ∧ j0 < j → st[r -- (i + j0) '] = st0[r0 -- (i0 + j0) ']) ,[st0, i0, r0, st, j, i, r] → [st, i, r, addarray(r0, ty, vals, st), j, i, r] ,F ,storearrays , ,get-alleq ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j = j + i])], [EXTRATERMS : (st, i, r, addarray(r0, ty, vals, st), j, i, r)]]