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Proof step 37 from proof cyclic-def-simple (previous step)

is_array(str, r, st), dups(refs1) ∨ r ∈ refs1, refs1 = [] ∨ 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ refs1 .first = st[r -- i '] .refval ∧ validrefs(str, refs1, st[r -- _type] .type .type, st) ⊦ r = jvmref, validrefs(str, r ' + refs1, mkclasstype(`java.lang.Object' .class), st), ¬ r ∈ refs1 ∧ ¬ dups(refs1)

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 36:
is_array(str, r, st) ∧ st[r -- _type] .type ≤ mkclasstype(`java.lang.Object' .class), is_array(str, r, st), dups(refs1) ∨ r ∈ refs1, refs1 = [] ∨ 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ refs1 .first = st[r -- i '] .refval ∧ validrefs(str, refs1, st[r -- _type] .type .type, st) ⊦ r = jvmref, refs1 = [] ∨ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ refs1 .first = st[r -- i '] .refval ∧ validrefs(str, refs1, st[r -- _type] .type .type, st)), ¬ r ∈ refs1 ∧ ¬ dups(refs1)

Rule argument

[crewrite-arg: validrefs-array , F , [st, ty, refs, r, str] → [st, mkclasstype(`java.lang.Object' .class), refs1, r, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_array(str, r, st) → ( st[r -- _type] .type ≤ mkclasstype(class) ↔ class = `java.lang.Object' .class)])], [EXTRATERMS : (st, mkclasstype(`java.lang.Object' .class), refs1, r, str)]]