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Proof step 15 from proof putArray-put (previous step)

∀ 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(# (val0 ' + vals0))) ', val]) = (putArray(vals0 + val ', r, j + 1, st)[r -- j ', val0])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ putArray(vals + val ', r, i, st) = putArray(vals, r, i, st[r -- (i + n→i(# vals)) ', val])
Proof step 14:
∀ 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(# (val0 ' + vals0))) ', val]) = (putArray(vals0, r, j + 1, st[r -- ((j + 1) + n→i(# vals0)) ', val])[r -- j ', val0])

Rule argument

[crewrite-arg: putAr-lastrec , F , [st, i, r, val, vals] → [st, j + 1, r, val, vals0] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, j + 1, r, val, vals0)]]