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Proof step 18 from proof putarray-addarray (previous step)

n→i(# vals) + j = i0 + 1, 0 ≤ i, 0 ≤ j, i ≤ i0 + 1, j ≤ i, (~1) ≤ i0, ∀ st, val, r, j, i, vals0. # vals0 < # vals → ( 0 ≤ i ∧ 0 ≤ j ∧ i ≤ j + n→i(# vals0) ∧ j ≤ i ∧ 0 ≤ j + n→i(# vals0) → putArray(vals0, r, j, addarray(r, val, i, st)) = addarray(r, mklist(val, i→n(j)) + vals0, 0, st)) ⊦ putArray(vals, r, j, addarray(r, val, i, st)) = (addarray(r, mklist(val, i→n(j)) + vals .butlast, 0, st)[r -- i0 ', vals .last]), vals = [], mklist(val, i→n(j)) + vals = []

User applied rule insert elim lemma

And obtained the following new goals

Proof step 17:
vals = vals1 + val0 ', n→i(# vals) + j = i0 + 1, 0 ≤ i, 0 ≤ j, i ≤ i0 + 1, j ≤ i, (~1) ≤ i0, ∀ st, val, r, j, i, vals0. # vals0 < # vals → ( 0 ≤ i ∧ 0 ≤ j ∧ i ≤ j + n→i(# vals0) ∧ j ≤ i ∧ 0 ≤ j + n→i(# vals0) → putArray(vals0, r, j, addarray(r, val, i, st)) = addarray(r, mklist(val, i→n(j)) + vals0, 0, st)) ⊦ putArray(vals, r, j, addarray(r, val, i, st)) = (addarray(r, mklist(val, i→n(j)) + vals1, 0, st)[r -- i0 ', val0]), vals = [], mklist(val, i→n(j)) + vals = []

Rule argument

[speclemmaarg: vals ≠ [] ,val = vals .last ∧ vals0 = vals .butlast ↔ vals = vals0 + val ' ,[vals, val, vals0] → [vals, val0, vals1] ,T ,list-last ,javavalues ,last-elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : vals ≠ [] ⊦ val = vals .last ∧ vals0 = vals .butlast ↔ vals = vals0 + val '])], [EXTRATERMS : (vals, val0, vals1)]]