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Proof step 6 from proof shift-1init-01 (previous step)

∀ r, r0, j, st, sk, val. r = r0 ∨ (addarray(r, vals0, j, st)[r0 -- sk, val]) = addarray(r, vals0, j, st[r0 -- sk, val]) ⊦ r = r0, (addarray(r, vals0, j + 1, st)[r -- j ', val0][r0 -- sk, val]) = (addarray(r, vals0, j + 1, st[r0 -- sk, val])[r -- j ', val0])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ rk ≠ rk0 → (st[rk0, val][rk, val0]) = (st[rk, val0][rk0, val])
Proof step 5:
r0 -- sk ≠ r -- j ', ∀ r, r0, j, st, sk, val. r = r0 ∨ (addarray(r, vals0, j, st)[r0 -- sk, val]) = addarray(r, vals0, j, st[r0 -- sk, val]) ⊦ r = r0, (addarray(r, vals0, j + 1, st)[r0 -- sk, val][r -- j ', val0]) = (addarray(r, vals0, j + 1, st[r0 -- sk, val])[r -- j ', val0])

Rule argument

[speclemmaarg: ,rk ≠ rk0 → (st[rk0, val][rk, val0]) = (st[rk, val0][rk0, val]) ,[val0, rk, val, rk0, st] → [val, r0 -- sk, val0, r -- j ', addarray(r, vals0, j + 1, st)] ,F ,store ,javastore ,rew ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0])], [EXTRATERMS : (val, r0 -- sk, val0, r -- j ', addarray(r, vals0, j + 1, st))]]