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Proof step 27 from proof validref-refs-last-valid-subset (previous step)

st0[r0 -- _length] = intval(i0), st[r0 -- _type] = typeval(mkarraytype(ty)), r0 -- _type ∈ st, ty ≤ ty0, i < i0, 0 ≤ i, validref(str, r0, mkarraytype(ty0), st), st ⊆ st0, 0 ≤ i0, r0 ∈ st, type∃(str, ty), okreftype(refval(r0), mkarraytype(ty), st), is_arrayref(r0, st[r0 -- _length] .intval, st), 0 ≤ st[r0 -- _length] .intval, ∀ j. ¬ j < 0 ∧ ¬ st[r0 -- _length] .intval ≤ j → okval(st[r0 -- j '], ty) ⊦ ty .jtelemtype = abstract_type, ty .jtelemtype = void_type, r0 = jvmref, r0 -- i ' ∈ st, noval .refval ∈ acc, r1 ≠ r2 ∧ ¬ r1 ∈ refs, ¬ r2 ∈ acc ∧ r2 ≠ r1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ is_arrayref(r, i, st) ↔ (∀ j. 0 ≤ j ∧ j < i → r -- j ' ∈ st)
Proof step 26:
st0[r0 -- _length] = intval(i0), st[r0 -- _type] = typeval(mkarraytype(ty)), r0 -- _type ∈ st, ty ≤ ty0, i < i0, 0 ≤ i, validref(str, r0, mkarraytype(ty0), st), st ⊆ st0, 0 ≤ i0, r0 ∈ st, type∃(str, ty), okreftype(refval(r0), mkarraytype(ty), st), ∀ j. 0 ≤ j ∧ j < st[r0 -- _length] .intval → r0 -- j ' ∈ st, 0 ≤ st[r0 -- _length] .intval, ∀ j. ¬ j < 0 ∧ ¬ st[r0 -- _length] .intval ≤ j → okval(st[r0 -- j '], ty) ⊦ ty .jtelemtype = abstract_type, ty .jtelemtype = void_type, r0 = jvmref, r0 -- i ' ∈ st, noval .refval ∈ acc, r1 ≠ r2 ∧ ¬ r1 ∈ refs, ¬ r2 ∈ acc ∧ r2 ≠ r1

Rule argument

[speclemmaarg: ,is_arrayref(r, i, st) ↔ (∀ j. 0 ≤ j ∧ j < i → r -- j ' ∈ st) ,[st, i, r] → [st, st[r0 -- _length] .intval, r0] ,F ,storearrays , ,is_arrayref ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, st[r0 -- _length] .intval, r0)]]