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Proof step 23 from proof putAr-lastrec (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ rk ≠ rk0 → (st[rk0, val][rk, val0]) = (st[rk, val0][rk0, val])
Proof step 22:
r -- ((i + 1) + n→i(# vals0)) ' ≠ r -- i ', putArray(vals0 + val ', r, i + 1, st[r -- i ', val0]) = (putArray(vals0, r, i + 1, st)[r -- ((i + 1) + n→i(# vals0)) ', val][r -- i ', val0]), ∀ val, r, i, st. putArray(vals0 + val ', r, i, st) = (putArray(vals0, r, i, st)[r -- (i + n→i(# vals0)) ', val]) ⊦ (putArray(vals0 + val ', r, i + 1, st)[r -- i ', val0]) = (putArray(vals0, r, i + 1, st)[r -- ((1 + n→i(# vals0)) + i) ', val][r -- i ', val0])

Rule argument

[speclemmaarg: ,rk ≠ rk0 → (st[rk0, val][rk, val0]) = (st[rk, val0][rk0, val]) ,[val0, rk, val, rk0, st] → [val, r -- ((i + 1) + n→i(# vals0)) ', 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 : ⊦ i = i + j ↔ j = 0], [CSIMPSEQ : ⊦ 0 ≠ n→i(m) + 1], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i])], [EXTRATERMS : (val, r -- ((i + 1) + n→i(# vals0)) ', val0, r -- i ', putArray(vals0, r, i + 1, st))]]