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Proof step 57 from proof putarray-addarray-override (previous step)

0 ≤ i, i + n→i(# vals) ≤ n→i(# vals0) ⊦ r0 -- fs ' ∈ addarray(r, ty, vals0, st) ↔ r0 -- fs ' ∈ 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 33:
fs ' ≠ _type, fs ' ≠ _length ⊦ r -- fs ' ∈ addarray(r0, ty, vals, st) ↔ r -- fs ' ∈ st
Proof step 55:
¬ (fs ' ≠ _type ∧ fs ' ≠ _length), 0 ≤ i, i + n→i(# vals) ≤ n→i(# vals0) ⊦ r0 -- fs ' ∈ addarray(r, ty, vals0, st) ↔ r0 -- fs ' ∈ addarray(r, ty, firstn(i→n(i), vals0) + vals + restn(i→n(i) + # vals, vals0), st)
Proof step 56:
fs ' ≠ _type, fs ' ≠ _length ⊦ r -- fs ' ∈ addarray(r0, ty, vals, st) ↔ r -- fs ' ∈ st

Rule argument

[crewrite-arg: in-init-06 , F , [st, vals, ty, r0, fs, r] → [st, vals0, ty, r, fs, r0] ]

Additional information

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