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Proof step 50 from proof addarray-addaray (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 36:
⊦ r ≠ r0 ∨ r = r0 ∧ is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type ∨ r = r0 ∧ is_indexkey(sk) ∧ (sk .index < 0 ∨ j ≤ sk .index) → (r0 -- sk ∈ addarray(r, ty, j, st) ↔ r0 -- sk ∈ st)
Proof step 37:
⊦ r -- _length ∈ addarray(r, ty, i, st)
Proof step 38:
⊦ r -- _length ∈ addarray(r0, ty, vals, st) ↔ r = r0 ∨ r -- _length ∈ st
Proof step 39:
⊦ r -- _length ∈ addarray(r, ty, vals, st)
Proof step 40:
⊦ r -- _type ∈ addarray(r, ty, i, st)
Proof step 41:
⊦ r -- _type ∈ addarray(r, ty, vals, st)
Proof step 49:
r ≠ r ∨ r = r ∧ is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type ∨ r = r ∧ is_indexkey(sk) ∧ (sk .index < 0 ∨ i ≤ sk .index), 0 ≤ i, is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type ∨ is_indexkey(sk) ∧ (sk .index < 0 ∨ i ≤ sk .index) ⊦ r -- sk ∈ st ↔ r -- sk ∈ addarray(r, ty, mklist(initial_value(ty), i→n(i)), st)

Rule argument

[crewrite-arg: in-1dim-other , F , [st, j, ty, r, sk, r0] → [st, i, ty, r, sk, r] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_fskey(sk) ↔ is_indexkey(sk)], [CSIMPSEQ : ⊦ is_indexkey(sk) → ¬ is_fskey(sk)], [CSIMPSEQ : ⊦ ¬ is_indexkey(sk) ↔ is_fskey(sk)])], [EXTRATERMS : (st, i, ty, r, sk, r)]]