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Proof step 33 from proof disjoint-forward-array (previous step)

st[r1 -- i '] = refval(r2), is_array(str, r1, st), path∃(str, r3, r0, st), path∃(str, r2, r0, st), r ∈ refs, r1 ∈ refs, i < st[r1 -- _length] .intval, is_arraytype(st[r1 -- _type] .type), 0 ≤ i, 0 < st[r1 -- _length] .intval, r3 ∈ refs, ∀ r4, r5, r6. ¬ r4 ∈ refs ∨ ¬ r5 ∈ refs ∨ r4 = r5 ∨ r6 = jvmref ∨ ¬ path∃(str, r4, r6, st) ∨ ¬ path∃(str, r5, r6, st) ⊦ r1 = jvmref, r = r1, r0 = jvmref, r3 = r2, r3 = r1, r1 = r0, junkref(str, r1, st), r2 ∈ refs, r2 ∈ refs -l r1, ∃ i0. ¬ i0 < 0 ∧ ¬ st[r1 -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r1 -- i0 ']) ∧ st[r1 -- i0 '] .refval ≠ jvmref ∧ st[st[r1 -- i0 '] .refval -- _type] .type ≤ st[r1 -- _type] .type .type ∧ path∃(str, st[r1 -- i0 '] .refval, r0, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Rule argument

[x0lemmaarg: spec-name: javatype instance-name: lemma-name: elim-01 antecedent: succedent: is_arraytype(ty) → (ty0 = ty .type ↔ ty = mkarraytype(ty0)) substlist: [ty, ty0] → [st[r1 -- _type] .type, ty] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_arraytype(ty) → ( ty0 = ty .type ↔ ty = mkarraytype(ty0))])], [EXTRATERMS : (st[r1 -- _type] .type, ty)]]