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Proof step 6 from proof get-first (previous step)

getarray(r, i, i0, st) .first = st[r -- i '], 0 < i0, 0 ≤ i0, ∀ j0, r, i, st. i→n(j0) < i→n(i0 + 1) → (0 < j0 → getarray(r, i, j0, st) .first = st[r -- i ']) ⊦ (getarray(r, i, i0, st) + st[r -- (i + i0) '] ') .first = getarray(r, i, i0, st) .first

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ vals ≠ [] → (vals + vals0) .first = vals .first
Proof step 4:
⊦ getarray(r, i, j, st) = [] ↔ j ≤ 0
Proof step 5:
⊦ getarray(r, i, 0, st) = []

Rule argument

[speclemmaarg: ,vals ≠ [] → (vals + vals0) .first = vals .first ,[vals0, vals] → [st[r -- (i + i0) '] ', getarray(r, i, i0, st)] ,F ,list ,javavalues ,first-01 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i ≤ j → (j ≤ i ↔ i = j)], [CSIMPFORWARD : ⊦ i < j ∧ i = i0 → i0 < j], [CSIMPFORWARD : ⊦ i < j ∧ j = i0 → i < i0], [CSIMPSEQ : ⊦ i + 0 = i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ [] + vals = vals], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPSEQ : ⊦ val ' .first = val])], [EXTRATERMS : (st[r -- (i + i0) '] ', getarray(r, i, i0, st))]]