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Proof step 12 from proof putArray-put (previous step)

0 ≤ (j + 1) + n→i(# vals0) ∧ 0 ≤ j + 1 ∧ (j + 1) + n→i(# vals0) ≤ (j + 1) + n→i(# vals0), ∀ j, r, st, val. 0 ≤ j → (putArray(vals0, r, j, st)[r -- (j + n→i(# vals0)) ', val]) = putArray(vals0 + val ', r, j, st), 0 ≤ j ⊦ (putArray(vals0, r, j + 1, st)[r -- j ', val0][r -- (j + n→i((# vals0) +1)) ', val]) = (putArray(vals0, r, j + 1, st)[r -- ((j + 1) + n→i(# vals0)) ', val][r -- j ', val0])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ 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] → [val0, r -- j ', val, r -- ((j + 1) + n→i(# vals0)) ', putArray(vals0, r, j + 1, st)] ,F ,store ,javastore ,rew ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ m +1 = m + 1], [CSIMPSEQ : ⊦ n→i(m + n) = n→i(m) + n→i(n)], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)], [CSIMPSEQ : ⊦ i ' = i0 ' ↔ i = i0], [CSIMPSEQ : ⊦ i = i + j ↔ j = 0], [CSIMPSEQ : ⊦ 0 ≠ n→i(m) + 1], [CSIMPSEQ : ⊦ i + j = j + i])], [EXTRATERMS : (val0, r -- j ', val, r -- ((j + 1) + n→i(# vals0)) ', putArray(vals0, r, j + 1, st))]]