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Proof step 17 from proof putarray-add-same (previous step)

is_indexkey(sk) ∧ (sk .index < 0 ∨ n→i(# vals) ≤ sk .index) ∨ is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type ⊦ r0 -- sk ∈ st ∨ is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < n→i(# vals) ↔ r0 -- sk ∈ addarray(r0, ty, vals, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ 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 16:
¬ (r0 ≠ r0 ∨ r0 = r0 ∧ is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type ∨ r0 = r0 ∧ is_indexkey(sk) ∧ (sk .index < 0 ∨ n→i(# vals) ≤ sk .index)), is_indexkey(sk) ∧ (sk .index < 0 ∨ n→i(# vals) ≤ sk .index) ∨ is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type ⊦ r0 -- sk ∈ st ∨ is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < n→i(# vals) ↔ r0 -- sk ∈ addarray(r0, ty, vals, st)

Rule argument

[crewrite-arg: add-in-other , F , [st, vals, ty, r, sk, r0] → [st, vals, ty, r0, sk, r0] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_indexkey(sk) → ¬ is_fskey(sk)], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)])], [EXTRATERMS : (st, vals, ty, r0, sk, r0)]]