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Proof step 12 from proof instore-afterputs (previous step)

instore(r, class, (sk1 × val) ' + fis0, st), r ∈ st, r -- sk ∈ st, unique_al(fis0), ∀ r0, st0, sk0, class0, r2. r0 ∈ st0 ∧ r0 -- sk0 ∈ st0 ∧ instore(r0, class0, fis0, st0) → _type = sk0 ∨ sk0 ∈ fis0 ∨ instore(r0, class0, fis0, st0[r0 -- sk0, refval(r2)]) ⊦ _type = sk, sk = sk1, _type = sk1, _type ∈ fis0, sk1 ∈ fis0, sk ∈ fis0, r -- sk1 ∈ st ∧ st[r -- sk1] = val ∧ instore(r, class, fis0, st[r -- sk, refval(r1)])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ instore(r, class, fv ' + fis, st) ↔ (r -- fv .1) × fv .2 ∈ st ∧ instore(r, class, fis, st)
Proof step 11:
(r -- (sk1 × val) .1) × (sk1 × val) .2 ∈ st ∧ instore(r, class, fis0, st), r ∈ st, r -- sk ∈ st, unique_al(fis0), ∀ r0, st0, sk0, class0, r2. r0 ∈ st0 ∧ r0 -- sk0 ∈ st0 ∧ instore(r0, class0, fis0, st0) → _type = sk0 ∨ sk0 ∈ fis0 ∨ instore(r0, class0, fis0, st0[r0 -- sk0, refval(r2)]) ⊦ _type = sk, sk = sk1, _type = sk1, _type ∈ fis0, sk1 ∈ fis0, sk ∈ fis0, r -- sk1 ∈ st ∧ st[r -- sk1] = val ∧ instore(r, class, fis0, st[r -- sk, refval(r1)])

Rule argument

[crewrite-arg: instore-rec-03 , F , [st, fis, fv, class, r] → [st, fis0, sk1 × val, class, r] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, fis0, sk1 × val, class, r)]]