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Proof step 4 from proof putArray-put-switch (previous step)

putArray(vals0, r, i + 1, st[r -- j ', val]) = (putArray(vals0, r, i + 1, st)[r -- j ', val]), 0 ≤ j, 0 ≤ i, n→i(# vals0) + i < j, ∀ i0, j0, r0, st0, val1. ¬ j0 < i0 + n→i(# vals0) ∧ ¬ j0 < 0 ∧ ¬ i0 < 0 → putArray(vals0, r0, i0, st0[r0 -- j0 ', val1]) = (putArray(vals0, r0, i0, st0)[r0 -- j0 ', val1]) ⊦ (putArray(vals0, r, i + 1, st)[r -- j ', val][r -- i ', val0]) = (putArray(vals0, r, i + 1, st)[r -- i ', val0][r -- j ', val])

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])

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPSEQ : ⊦ i ' = i0 ' ↔ i = i0], [CSIMPSEQ : ⊦ (st[rk, val][rk, val0]) = st[rk, val0]], [CSIMPSEQ : ⊦ i + j < j ↔ i < 0], [CSIMPSEQ : ⊦ ¬ n→i(n) < 0], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i])], [EXTRATERMS : (val, r -- j ', val0, r -- i ', putArray(vals0, r, i + 1, st))]]