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Proof step 47 from proof unchNorec-validrefs (previous step)

st[r -- _length] = st0[r -- _length], st[r -- _type] = st0[r -- _type], st0[r -- _type] .type = mkarraytype(ty0), unchangedNorec(r, st, st0), mkarraytype(ty0) ≤ ty, is_array(str, r, st), ∀ str, ty, st, st0. validrefs(str, refs0, ty, st) ∧ (∀ r. r ∈ refs0 → unchangedNorec(r, st, st0)) → validrefs(str, refs0, ty, st0), refs0 = [] ∨ 0 ≤ i ∧ i < st0[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ refs0 .first = st[r -- i '] .refval ∧ validrefs(str, refs0, ty0, st), ∀ r0. r0 ∈ refs0 → unchangedNorec(r0, st, st0) ⊦ r = jvmref, validrefs(str, r ' + refs0, ty, st0)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[x0lemmaarg: spec-name: cyclic instance-name: lemma-name: validrefs-array antecedent: succedent: 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))) substlist: [st, ty, refs, r, str] → [st0, ty, refs0, r, str] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 1)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st0, ty, refs0, r, str)]]