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Proof step 30 from proof validrefs-addobj-notin (previous step)

is_array(str, r0, st), st[r0 -- _type] .type ≤ ty, ∀ str, ty, st, r, class, fis. validrefs(str, acc, ty, st) → r ∈ acc ∨ validrefs(str, acc, ty, addobj(r, class, fis, st)), acc = [] ∨ 0 ≤ i ∧ i < st[r0 -- _length] .intval ∧ is_referencevalue(st[r0 -- i ']) ∧ acc .first = st[r0 -- i '] .refval ∧ validrefs(str, acc, st[r0 -- _type] .type .type, st) ⊦ r0 = jvmref, r = r0, validrefs(str, r0 ' + acc, ty, addobj(r, class, fis, st)), r ∈ acc

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( validrefs(str, r ' + refs, ty, st) ↔ refs = [] ∨ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ refs .first = st[r -- i '] .refval ∧ validrefs(str, refs, st[r -- _type] .type .type, st)))
Proof step 29:
is_array(str, r0, addobj(r, class, fis, st)) ∧ (addobj(r, class, fis, st)[r0 -- _type]) .type ≤ ty, is_array(str, r0, st), st[r0 -- _type] .type ≤ ty, ∀ str, ty, st, r, class, fis. validrefs(str, acc, ty, st) → r ∈ acc ∨ validrefs(str, acc, ty, addobj(r, class, fis, st)), acc = [] ∨ 0 ≤ i ∧ i < st[r0 -- _length] .intval ∧ is_referencevalue(st[r0 -- i ']) ∧ acc .first = st[r0 -- i '] .refval ∧ validrefs(str, acc, st[r0 -- _type] .type .type, st) ⊦ r0 = jvmref, r = r0, acc = [] ∨ (∃ i. 0 ≤ i ∧ i < (addobj(r, class, fis, st)[r0 -- _length]) .intval ∧ is_referencevalue(addobj(r, class, fis, st)[r0 -- i ']) ∧ acc .first = (addobj(r, class, fis, st)[r0 -- i ']) .refval ∧ validrefs(str, acc, (addobj(r, class, fis, st)[r0 -- _type]) .type .type, addobj(r, class, fis, st))), r ∈ acc

Rule argument

[crewrite-arg: validrefs-array , F , [st, ty, refs, r, str] → [addobj(r, class, fis, st), ty, acc, r0, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ≠ r0 → ( is_array (str, r, addobj(r0, class, fis, st)) ↔ is_array(str, r, st))], [CSIMPSEQ : ⊦ r ≠ r0 → (addobj(r, class1, fis, st) [r0 -- sk ] ) = st[r0 -- sk]])], [EXTRATERMS : (addobj(r, class, fis, st), ty, acc, r0, str)]]