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Proof step 56 from proof pathex-put-pathex-array-refval (previous step)

refs1 + r0 ' = r1 ' + refs0, st[r0 -- _type] .type = mkarraytype(ty), is_array(str, r0, st[r0 -- i ', refval(r3)]), i < st[r0 -- _length] .intval, validrefs(str, r3 ', ty, st), validrefs(str, r ' + refs1 + r0 ' + r3 ', st[r -- _type] .type, st[r0 -- i ', refval(r3)]), path∃(str, r, r0, st), validref(str, r3, ty, st), 0 < st[r0 -- _length] .intval, 0 ≤ i, validrefs(str, refs1 + r0 ' + r3 ', st[r1 -- _type] .type, st[r0 -- i ', refval(r3)]) ⊦ r0 = jvmref, r = r0, r0 = r3, r = r3, r3 = jvmref, r ∈ refs1, r0 ∈ refs1, dups(refs1), r3 ∈ refs1, is_valid_ref(str, r3, st), ¬ r1 ∈ refs1 ∧ r1 ≠ r0, r0 ≠ r1 ∧ ¬ r0 ∈ refs0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: validrefs-one antecedent: succedent: validrefs(str, r ', ty, st) ↔ r = jvmref ∨ r ≠ jvmref ∧ is_valid_ref(str, r, st) ∧ st[r -- _type] .type ≤ ty substlist: [st, ty, r, str] → [st, ty, r3, str] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((0, 0, 4)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, ty, r3, str)]]