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Proof step 46 from proof validrefs-not-contains (previous step)

is_array(str, r, st), validrefs(str, r ' + r0 ', ty, st), st[r -- _type] .type ≤ ty ⊦ r0 = jvmref, r = r0, r = jvmref, contains(str, st[r -- _type] .type, st[r0 -- _type] .type)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 30:
⊦ 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)))
Proof step 45:
is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty, is_array(str, r, st), r0 ' = [] ∨ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ r0 ' .first = st[r -- i '] .refval ∧ validrefs(str, r0 ', st[r -- _type] .type .type, st)), st[r -- _type] .type ≤ ty ⊦ r0 = jvmref, r = r0, r = jvmref, contains(str, st[r -- _type] .type, st[r0 -- _type] .type)

Rule argument

[speclemmaarg: , 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))) ,[st, ty, refs, r, str] → [st, ty, r0 ', r, str] ,F ,cyclic , ,validrefs-array ]

Additional information

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