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Proof step 105 from proof validrefs-not-contains (previous step)

is_obj(str, r, st), validrefs(str, r ' + r0 ' + refs0 + r1 ', ty, st), st[r -- _type] .type ≤ ty, ∀ str0, st0, ty0. ¬ contains(str0, st0[r0 -- _type] .type, st0[r1 -- _type] .type) ∧ r0 ≠ r1 → ¬ validrefs(str0, r0 ' + refs0 + r1 ', ty0, st0) ⊦ r1 = jvmref, r = r1, r = jvmref, contains(str, st[r -- _type] .type, st[r1 -- _type] .type)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[speclemmaarg: , is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( validrefs(str, r ' + refs, ty, st) ↔ refs = [] ∨ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ refs .first = st[r -- fs '] .refval ∧ validrefs(str, refs, fs .type, st))) ,[st, ty, refs, r, str] → [st, ty, r0 ' + refs0 + r1 ', r, str] ,F ,cyclic , ,validrefs-class ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, ty, r0 ' + refs0 + r1 ', r, str)]]