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Proof step 10 from proof addarray-is-putarray (previous step)

0 ≤ i1, ∀ st, val, r, i0. i→n(i0) < i→n(i1 + 1) → (0 ≤ i0 → addarray(r, val, i0, st) = putArray(mklist(val, i→n(i0)), r, 0, st)) ⊦ (addarray(r, val, i1, st)[r -- i1 ', val]) = putArray(mklist(val, i→n(i1)) + val ', r, 0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ putArray(vals + val ', r, i, st) = putArray(vals, r, i, st[r -- (i + n→i(# vals)) ', val])
Proof step 9:
0 ≤ i1, ∀ st, val, r, i0. i→n(i0) < i→n(i1 + 1) → (0 ≤ i0 → addarray(r, val, i0, st) = putArray(mklist(val, i→n(i0)), r, 0, st)) ⊦ (addarray(r, val, i1, st)[r -- i1 ', val]) = putArray(mklist(val, i→n(i1)), r, 0, st[r -- (0 + n→i(# mklist(val, i→n(i1)))) ', val])

Rule argument

[speclemmaarg: , putArray(vals + val ', r, i, st) = putArray(vals, r, i, st[r -- (i + n→i(# vals)) ', val]) ,[st, i, r, val, vals] → [st, 0, r, val, mklist(val, i→n(i1))] ,F ,storearrays , ,putAr-lastrec ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, 0, r, val, mklist(val, i→n(i1)))]]