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Proof step 8 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)), r, 0, st[r -- i1 ', val])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ 0 ≤ j ∧ 0 ≤ i ∧ i + n→i(# vals) ≤ j → putArray(vals, r, i, st[r -- j ', val]) = (putArray(vals, r, i, st)[r -- j ', val])
Proof step 7:
0 ≤ i1 ∧ 0 ≤ 0 ∧ 0 + n→i(# mklist(val, i→n(i1))) ≤ i1, 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 -- i1 ', val])

Rule argument

[speclemmaarg: , 0 ≤ j ∧ 0 ≤ i ∧ i + n→i(# vals) ≤ j → putArray(vals, r, i, st[r -- j ', val]) = (putArray(vals, r, i, st)[r -- j ', val]) ,[val, j, st, i, r, vals] → [val, i1, st, 0, r, mklist(val, i→n(i1))] ,F ,storearrays , ,putArray-put-switch ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ # mklist(val, n) = n], [CSIMPSEQ : ⊦ 0 ≤ i → n→i(i→n(i)) = i], [CSIMPSEQ : ⊦ i + 0 = i], [CSIMPSEQ : ⊦ ¬ i < i])], [EXTRATERMS : (val, i1, st, 0, r, mklist(val, i→n(i1)))]]