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Proof step 10 from proof validref-pseq (previous step)

okreftype(refval(r1), ty, st1), ps=(r, st, r1, st1) ⊦ junkref(`docs2store', r1, st1), junkref(`docs2store', r, st), okreftype(refval(r), ty, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ ps=(r, st, r1, st1) ↔ r = jvmref ∧ r1 = jvmref ∨ r ≠ jvmref ∧ r1 ≠ jvmref ∧ st[r -- _type] = st1[r1 -- _type] ∧ ( is_classtype(st[r -- _type] .type) → (∀ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) → ps=(st[r -- fs '] .refval, st, st1[r1 -- fs '] .refval, st1)) ∧ (∀ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ ¬ is_referencevalue(st[r -- fs ']) → st[r -- fs '] = st1[r1 -- fs '])) ∧ ( is_arraytype(st[r -- _type] .type) → st[r -- _length] .intval = st1[r1 -- _length] .intval ∧ (∀ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) → ps=(st[r -- i '] .refval, st, st1[r1 -- i '] .refval, st1)) ∧ (∀ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ ¬ is_referencevalue(st[r -- i ']) → st[r -- i '] = st1[r1 -- i ']))
Proof step 9:
okreftype(refval(r1), ty, st1), r = jvmref ∧ r1 = jvmref ∨ r ≠ jvmref ∧ r1 ≠ jvmref ∧ st[r -- _type] = st1[r1 -- _type] ∧ ( is_classtype(st[r -- _type] .type) → (∀ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) → ps=(st[r -- fs '] .refval, st, st1[r1 -- fs '] .refval, st1)) ∧ (∀ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ ¬ is_referencevalue(st[r -- fs ']) → st[r -- fs '] = st1[r1 -- fs '])) ∧ ( is_arraytype(st[r -- _type] .type) → st[r -- _length] .intval = st1[r1 -- _length] .intval ∧ (∀ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) → ps=(st[r -- i '] .refval, st, st1[r1 -- i '] .refval, st1)) ∧ (∀ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ ¬ is_referencevalue(st[r -- i ']) → st[r -- i '] = st1[r1 -- i '])) ⊦ junkref(`docs2store', r1, st1), junkref(`docs2store', r, st), okreftype(refval(r), ty, st)

Rule argument

[crewrite-arg: pseq-def, F, [st1, r1, st, r] → [st1, r1, st, r]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st1, r1, st, r)]]