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Proof step 42 from proof putarray-addarray-override (previous step)

fs ' = _type, i + n→i(# vals) ≤ n→i(# vals0), 0 ≤ i ⊦ r0 -- _type ∈ addarray(r, ty, vals0, st) ↔ r0 -- _type ∈ addarray(r, ty, firstn(i→n(i), vals0) + vals + restn(i→n(i) + # vals, vals0), st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 34:
⊦ 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 35:
⊦ r -- _type ∈ addarray(r, ty, vals, st)
Proof step 41:
r ≠ r0 ∨ r = r0 ∧ is_fskey(_type) ∧ _type ≠ _length ∧ _type ≠ _type ∨ r = r0 ∧ is_indexkey(_type) ∧ (_type .index < 0 ∨ n→i(# vals0) ≤ _type .index), fs ' = _type, i + n→i(# vals) ≤ n→i(# vals0), 0 ≤ i ⊦ r0 -- _type ∈ st ↔ r0 -- _type ∈ addarray(r, ty, firstn(i→n(i), vals0) + vals + restn(i→n(i) + # vals, vals0), st)

Rule argument

[crewrite-arg: add-in-other , F , [st, vals, ty, r, sk, r0] → [st, vals0, ty, r, _type, r0] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, vals0, ty, r, _type, r0)]]