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Proof step 133 from proof validrefs-put-notin-03 (previous step)

is_valid_ref(str, r, st) ↔ is_valid_ref(str, r, st[r -- sk, val]), list2set(refs1) ∩ list2set(refs0) = ∅, is_valid_ref(str, r1, st), st[r1 -- _type] .type ≤ ty, ∀ str0, r2, st0, sk0, val0, refs, r3, ty0. (is_valid_ref(str0, r2, st0) ↔ is_valid_ref(str0, r2, st0[r2 -- sk0, val0])) ∧ list2set(refs0) ∩ list2set(refs) = ∅ → val0 .refval = r3 ∨ r3 = st0[r2 -- sk0] .refval ∨ sk0 = _type ∨ sk0 = _length ∨ (validrefs(str0, refs0 + r2 ' + r3 ' + refs, ty0, st0[r2 -- sk0, val0]) ↔ validrefs(str0, refs0 + r2 ' + r3 ' + refs, ty0, st0)) ∨ r2 = r3 ∨ r3 ∈ refs0 ∨ r2 ∈ refs ∨ r2 ∈ refs0 ∨ dups(refs) ∨ r3 ∈ refs ⊦ r = r0, val .refval = r0, r0 = st[r -- sk] .refval, sk = _type, sk = _length, validrefs(str, (r1 ' + refs0) + r ' + r0 ' + refs1, ty, st[r -- sk, val]) ↔ validrefs(str, (r1 ' + refs0) + r ' + r0 ' + refs1, ty, st), r0 = r1, r = r1, r1 = jvmref, dups(refs1), r0 ∈ refs1, r1 ∈ refs1, dups(refs0), r1 ∈ refs0, r0 ∈ refs0, r ∈ refs1, r ∈ refs0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[x0lemmaarg: spec-name: addfuns instance-name: lemma-name: is_valid_ref-def antecedent: succedent: is_valid_ref(str, r, st) ↔ ¬ ¬ ( is_valid_ref(r, st) ∧ (is_obj(str, r, st) ∨ is_array(str, r, st))) substlist: [st, r, str] → [st, r1, str] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 2)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, r1, str)]]