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Proof step 35 from proof instore-afterputs (previous step)

instore(r, class, (sk × val) ' + fv ' + fis0, st), unique_al(fv ' + fis0), ∀ r0, class0, sk0, val0, st0, r2. instore(r0, class0, (sk0 × val0) ' + fis0, st0) ∧ unique_al(fis0) → instore(r0, class0, (sk0 × refval(r2)) ', st0[r0 -- sk0, refval(r2)]) ∨ _type = sk0 ∨ sk0 ∈ fis0 ⊦ _type = sk, instore(r, class, (sk × refval(r1)) ', st[r -- sk, refval(r1)]), _type ∈ fv ', _type ∈ fis0, sk ∈ fv ', sk ∈ fis0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 27:
⊦ instore(r, class, fv ' + fis, st) ↔ (r -- fv .1) × fv .2 ∈ st ∧ instore(r, class, fis, st)
Proof step 34:
(r -- (sk × val) .1) × (sk × val) .2 ∈ st ∧ instore(r, class, fv ' + fis0, st), unique_al(fv ' + fis0), ∀ r0, class0, sk0, val0, st0, r2. instore(r0, class0, (sk0 × val0) ' + fis0, st0) ∧ unique_al(fis0) → instore(r0, class0, (sk0 × refval(r2)) ', st0[r0 -- sk0, refval(r2)]) ∨ _type = sk0 ∨ sk0 ∈ fis0 ⊦ _type = sk, instore(r, class, (sk × refval(r1)) ', st[r -- sk, refval(r1)]), _type ∈ fv ', _type ∈ fis0, sk ∈ fv ', sk ∈ fis0

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, fv ' + fis0, sk × val, class, r)]]