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Proof step 17 from proof add-putbar-rew (previous step)

⊦ r = r0, (r1 -- fs ' ∈ addobj(r0, class, fis, st) ↔ r1 -- fs ' ∈ addobj(r0, class, fis, putByteArray(bytes, r, i, st))) ∧ (addobj(r0, class, fis, st)[r1 -- fs ']) = (addobj(r0, class, fis, putByteArray(bytes, r, i, st))[r1 -- fs '])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ r ≠ r0 → (r -- sk ∈ addobj(r0, class1, fis, st) ↔ r -- sk ∈ st)
Proof step 14:
¬ r1 ≠ r0 ⊦ r = r0, (r1 -- fs ' ∈ addobj(r0, class, fis, st) ↔ r1 -- fs ' ∈ addobj(r0, class, fis, putByteArray(bytes, r, i, st))) ∧ (addobj(r0, class, fis, st)[r1 -- fs ']) = (addobj(r0, class, fis, putByteArray(bytes, r, i, st))[r1 -- fs '])
Proof step 15:
⊦ r ≠ r0 → (r -- sk ∈ addobj(r0, class1, fis, st) ↔ r -- sk ∈ st)
Proof step 16:
⊦ r ≠ r0 → (addobj(r, class1, fis, st)[r0 -- sk]) = st[r0 -- sk]

Rule argument

[crewrite-arg: add-in-04 , F , [st, fis, class1, r0, sk, r] → [st, fis, class, r0, fs ', r1] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r0 -- fs ' ∈ putByteArray(bytes, r, j, st) ↔ r0 -- fs ' ∈ st], [CSIMPSEQ : ⊦ (putByteArray(bytes, r, j, st) [r0 -- fs ' ] ) = st[r0 -- fs ']])], [EXTRATERMS : (st, fis, class, r0, fs ', r1)]]