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Proof step 48 from proof addarray-addaray (previous step)

r -- sk ∈ addarray(r, ty, mklist(initial_value(ty), i→n(i)), st), 0 ≤ i, is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type ∨ is_indexkey(sk) ∧ (sk .index < 0 ∨ i ≤ sk .index) ⊦ r -- sk ∈ st

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 44:
⊦ r ≠ r0 ∨ r = r0 ∧ is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type ∨ r = r0 ∧ is_indexkey(sk) ∧ (sk .index < 0 ∨ n→i(# vals) ≤ sk .index) → (r0 -- sk ∈ addarray(r, ty, vals, st) ↔ r0 -- sk ∈ st)
Proof step 47:
¬ ( r ≠ r ∨ r = r ∧ is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type ∨ r = r ∧ is_indexkey(sk) ∧ (sk .index < 0 ∨ n→i(# mklist(initial_value(ty), i→n(i))) ≤ sk .index)), r -- sk ∈ addarray(r, ty, mklist(initial_value(ty), i→n(i)), st), 0 ≤ i, is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type ∨ is_indexkey(sk) ∧ (sk .index < 0 ∨ i ≤ sk .index) ⊦ r -- sk ∈ st

Rule argument

[crewrite-arg: add-in-other , F , [st, vals, ty, r, sk, r0] → [st, mklist(initial_value(ty), i→n(i)), ty, r, sk, r] ]

Additional information

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