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Proof step 222 from proof putarray-addarray-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 122:
⊦ rk .ref ≠ r → (addarray(r, ty, vals, st)[rk]) = st[rk]
Proof step 216:
¬ rk .ref ≠ r, 0 ≤ n→i(# vals) + i, 0 ≤ j, 0 ≤ i, i ≤ j, j ≤ n→i(# vals) + i ⊦ rk = r -- _length, (rk ∈ putArray(vals, r, i, addarray(r, ty, j, st)) ↔ rk ∈ addarray(r, ty, mklist(initial_value(ty), i→n(i)) + vals, st)) ∧ (putArray(vals, r, i, addarray(r, ty, j, st))[rk]) = (addarray(r, ty, mklist(initial_value(ty), i→n(i)) + vals, st)[rk])
Proof step 221:
rk .ref ≠ r, 0 ≤ n→i(# vals) + i, 0 ≤ j, 0 ≤ i, i ≤ j, j ≤ n→i(# vals) + i ⊦ rk = r -- _length, (rk ∈ putArray(vals, r, i, addarray(r, ty, j, st)) ↔ rk ∈ addarray(r, ty, mklist(initial_value(ty), i→n(i)) + vals, st)) ∧ (putArray(vals, r, i, addarray(r, ty, j, st))[rk]) = st[rk]

Rule argument

[crewrite-arg: add-at-01 , F , [rk, st, vals, ty, r] → [rk, st, mklist(initial_value(ty), i→n(i)) + vals, ty, r] ]

Additional information

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