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Proof step 62 from proof validref-refs-last-valid-subset (previous step)

acc + r1 ' = r2 ' + refs, st0[r0 -- i '] = refval(r2), st[r0 -- _type] = typeval(mkarraytype(ty0)), st0[r0 -- _type] = typeval(mkarraytype(ty0)), type∃(str, ty0), i < st0[r0 -- _length] .intval, validrefs(str, r2 ' + refs, ty0, st0), 0 ≤ i, 0 < st0[r0 -- _length] .intval, r0 ∈ st0, mkarraytype(ty0) ≤ ty, validref(str, r0, mkarraytype(ty0), st), st ⊆ st0, r0 -- _type ∈ st0, okarray(r0, ty0, st0), ∀ str, r, st, st0, r1, ty. validref(str, r, st[r -- _type] .type, st) ∧ st ⊆ st0 ∧ r ∈ acc ∧ validrefs(str, acc + r1 ', ty, st0) → validref(str, r1, st[r1 -- _type] .type, st) ⊦ r0 = jvmref, ty0 .jtelemtype = void_type, ty0 .jtelemtype = abstract_type, validref(str, r1, st[r1 -- _type] .type, st), r1 ≠ r2 ∧ ¬ r1 ∈ refs, ¬ r2 ∈ acc ∧ r2 ≠ r1, ¬ validref(str, st[r0 -- i '] .refval, ty0, st) ∧ ¬ st[r0 -- _length] .intval ≤ i

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ okarray(r, ty, st) ↔ okreftype(refval(r), mkarraytype(ty), st) ∧ r ≠ jvmref ∧ r -- _length ∈ st ∧ is_integervalue(st[r -- _length]) ∧ 0 ≤ st[r -- _length] .intval ∧ is_arrayref(r, st[r -- _length] .intval, st) ∧ (∀ j. 0 ≤ j ∧ j < st[r -- _length] .intval → oktype(st[r -- j '], ty, st))
Proof step 61:
acc + r1 ' = r2 ' + refs, st0[r0 -- i '] = refval(r2), st[r0 -- _type] = typeval(mkarraytype(ty0)), st0[r0 -- _type] = typeval(mkarraytype(ty0)), type∃(str, ty0), i < st0[r0 -- _length] .intval, validrefs(str, r2 ' + refs, ty0, st0), 0 ≤ i, 0 < st0[r0 -- _length] .intval, r0 ∈ st0, mkarraytype(ty0) ≤ ty, validref(str, r0, mkarraytype(ty0), st), st ⊆ st0, r0 -- _type ∈ st0, okreftype(refval(r0), mkarraytype(ty0), st0) ∧ r0 ≠ jvmref ∧ r0 -- _length ∈ st0 ∧ is_integervalue(st0[r0 -- _length]) ∧ 0 ≤ st0[r0 -- _length] .intval ∧ is_arrayref(r0, st0[r0 -- _length] .intval, st0) ∧ (∀ j. 0 ≤ j ∧ j < st0[r0 -- _length] .intval → oktype(st0[r0 -- j '], ty0, st0)), ∀ str, r, st, st0, r1, ty. validref(str, r, st[r -- _type] .type, st) ∧ st ⊆ st0 ∧ r ∈ acc ∧ validrefs(str, acc + r1 ', ty, st0) → validref(str, r1, st[r1 -- _type] .type, st) ⊦ r0 = jvmref, ty0 .jtelemtype = void_type, ty0 .jtelemtype = abstract_type, validref(str, r1, st[r1 -- _type] .type, st), r1 ≠ r2 ∧ ¬ r1 ∈ refs, ¬ r2 ∈ acc ∧ r2 ≠ r1, ¬ validref(str, st[r0 -- i '] .refval, ty0, st) ∧ ¬ st[r0 -- _length] .intval ≤ i

Rule argument

[speclemmaarg: , okarray(r, ty, st) ↔ okreftype(refval(r), mkarraytype(ty), st) ∧ r ≠ jvmref ∧ r -- _length ∈ st ∧ is_integervalue(st[r -- _length]) ∧ 0 ≤ st[r -- _length] .intval ∧ is_arrayref(r, st[r -- _length] .intval, st) ∧ (∀ j. 0 ≤ j ∧ j < st[r -- _length] .intval → oktype(st[r -- j '], ty, st)) ,[st, ty, r] → [st0, ty0, r0] ,F ,okfuns , ,okarrayNotNull ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st0, ty0, r0)]]