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Proof step 43 from proof unchNorec-validrefs (previous step)

st0[r -- _type] .type = mkarraytype(ty0), st[r -- _type] = st0[r -- _type], st[r -- _length] = st0[r -- _length], is_referencevalue(st[r -- i ']), i < st0[r -- _length] .intval, is_array(str, r, st), unchangedNorec(r, st, st0), mkarraytype(ty0) ≤ ty, is_array(str, r, st0), 0 < st0[r -- _length] .intval, 0 ≤ i, validrefs(str, st[r -- i '] .refval ' + refs, ty0, st), ∀ str0, ty1, st1, st2. validrefs(str0, st[r -- i '] .refval ' + refs, ty1, st1) ∧ (∀ r0. r0 = st[r -- i '] .refval ∨ r0 ∈ refs → unchangedNorec(r0, st1, st2)) → validrefs(str0, st[r -- i '] .refval ' + refs, ty1, st2), ∀ r0. r0 = st[r -- i '] .refval ∨ r0 ∈ refs → unchangedNorec(r0, st, st0) ⊦ r = jvmref, ∃ i0. ¬ i0 < 0 ∧ ¬ st0[r -- _length] .intval ≤ i0 ∧ is_referencevalue(st0[r -- i0 ']) ∧ st[r -- i '] .refval = st0[r -- i0 '] .refval ∧ validrefs(str, st[r -- i '] .refval ' + refs, ty0, st0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Rule argument

[x0lemmaarg: spec-name: javavalue instance-name: lemma-name: elim-13 antecedent: succedent: is_referencevalue(val) → (r = val .refval ↔ val = refval(r)) substlist: [val, r] → [st[r -- i '], r1] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_referencevalue(val) → ( r = val .refval ↔ val = refval(r))])], [EXTRATERMS : (st[r -- i '], r1)]]