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Proof step 213 from proof putarray-addarray-01 (previous step)

0 ≤ n→i(# vals) + i, 0 ≤ j, 0 ≤ i, i ≤ j, j ≤ n→i(# vals) + i ⊦ sk = _length, (r -- sk ∈ putArray(vals, r, i, addarray(r, ty, j, st)) ↔ r -- sk ∈ addarray(r, ty, mklist(initial_value(ty), i→n(i)) + vals, st)) ∧ (putArray(vals, r, i, addarray(r, ty, j, st))[r -- sk]) = (addarray(r, ty, mklist(initial_value(ty), i→n(i)) + vals, st)[r -- sk])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 123:
⊦ is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type → (r -- sk ∈ addarray(r, ty, vals, st) ↔ r -- sk ∈ st)
Proof step 202:
¬ (is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type), 0 ≤ n→i(# vals) + i, 0 ≤ j, 0 ≤ i, i ≤ j, j ≤ n→i(# vals) + i ⊦ sk = _length, (r -- sk ∈ putArray(vals, r, i, addarray(r, ty, j, st)) ↔ r -- sk ∈ addarray(r, ty, mklist(initial_value(ty), i→n(i)) + vals, st)) ∧ (putArray(vals, r, i, addarray(r, ty, j, st))[r -- sk]) = (addarray(r, ty, mklist(initial_value(ty), i→n(i)) + vals, st)[r -- sk])
Proof step 212:
is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type, 0 ≤ n→i(# vals) + i, 0 ≤ j, 0 ≤ i, i ≤ j, j ≤ n→i(# vals) + i ⊦ sk = _length, (r -- sk ∈ putArray(vals, r, i, addarray(r, ty, j, st)) ↔ r -- sk ∈ st) ∧ (putArray(vals, r, i, addarray(r, ty, j, st))[r -- sk]) = (addarray(r, ty, mklist(initial_value(ty), i→n(i)) + vals, st)[r -- sk])

Rule argument

[crewrite-arg: add-in-fskey , F , [st, vals, ty, sk, r] → [st, mklist(initial_value(ty), i→n(i)) + vals, ty, sk, r] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, mklist(initial_value(ty), i→n(i)) + vals, ty, sk, r)]]