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Proof step 13 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((# 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 10:
⊦ 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 12:
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])

Rule argument

[crewrite-arg: putArray-put-switch , F , [val, j, st, i, r, vals] → [val, (j + 1) + n→i(# vals0), st, j + 1, r, vals0] ]

Additional information

[[CONCRETESIMPRULES : ([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 : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ ((* j)) ≤ i0 + ((* j0)) ↔ j - j0 ≤ i0], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : i0 ≠ 0, i0 ≤ i ⊦ ((* i)) ≤ j → ((* i0)) ≤ j], [CSIMPSEQ : ⊦ i + j ≤ i0 + j ↔ i ≤ i0], [CSIMPSEQ : ⊦ ¬ i < i], [CSIMPFORWARD : ⊦ i < ((* j)) ∧ j < 0 → i < 0], [CSIMPFORWARD : ⊦ i < j ∧ j ≤ j0 → i < j0], [CSIMPSEQ : ⊦ i + j < j ↔ i < 0], [CSIMPSEQ : ⊦ ¬ n→i(n) < 0], [CSIMPSEQ : ⊦ i + j = j + i])], [EXTRATERMS : (val, (j + 1) + n→i(# vals0), st, j + 1, r, vals0)]]