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Proof step 43 from proof add-putbar-rew (previous step)

⊦ r = r0, r = r1, (r1 -- i0 ' ∈ addobj(r0, class, fis, st) ↔ r1 -- i0 ' ∈ addobj(r0, class, fis, putByteArray(bytes, r, i, st))) ∧ (addobj(r0, class, fis, st)[r1 -- i0 ']) = (addobj(r0, class, fis, putByteArray(bytes, r, i, st))[r1 -- i0 '])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 31:
⊦ r ≠ r0 → (addobj(r, class1, fis, st)[r0 -- sk]) = st[r0 -- sk]
Proof step 40:
¬ r0 ≠ r1 ⊦ r = r0, r = r1, (r1 -- i0 ' ∈ addobj(r0, class, fis, st) ↔ r1 -- i0 ' ∈ addobj(r0, class, fis, putByteArray(bytes, r, i, st))) ∧ (addobj(r0, class, fis, st)[r1 -- i0 ']) = (addobj(r0, class, fis, putByteArray(bytes, r, i, st))[r1 -- i0 '])
Proof step 41:
⊦ r ≠ r0 → (r -- sk ∈ addobj(r0, class1, fis, st) ↔ r -- sk ∈ st)
Proof step 42:
⊦ r ≠ r0 → (addobj(r, class1, fis, st)[r0 -- sk]) = st[r0 -- sk]

Rule argument

[crewrite-arg: add-ref , F , [sk, r0, st, fis, class1, r] → [i0 ', r1, st, fis, class, r0] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ≠ r0 → ( r0 -- sk ∈ putByteArray (bytes, r, j, st) ↔ r0 -- sk ∈ st)], [CSIMPSEQ : ⊦ r ≠ r0 → (putByteArray(bytes, r, j, st) [r0 -- sk ] ) = st[r0 -- sk]])], [EXTRATERMS : (i0 ', r1, st, fis, class, r0)]]