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Proof step 35 from proof validrefs-delcycle (previous step)

refs1 .last = jvmref, acc + r ' = r1 ' + refs, st[r0 -- i '] = refval(r1), is_array(str, r0, st), st[r0 -- _type] .type ≤ ty, i < st[r0 -- _length] .intval, validrefs(str, acc + r ' + refs0 + r ' + refs1, st[r0 -- _type] .type .type, st), 0 ≤ i, 0 < st[r0 -- _length] .intval, ∀ str, r, refs0, refs1, ty, st. validrefs(str, acc + r ' + refs0 + r ' + refs1, ty, st) ∧ refs1 ≠ [] ∧ refs1 .last = jvmref → validrefs(str, acc + r ' + refs1, ty, st) ⊦ r0 = jvmref, refs1 = [], validrefs(str, (r0 ' + acc) + r ' + refs1, ty, st), r ≠ r1 ∧ ¬ r ∈ refs, ¬ r1 ∈ acc ∧ r1 ≠ r

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 34:
is_array(str, r0, st) ∧ st[r0 -- _type] .type ≤ ty, refs1 .last = jvmref, acc + r ' = r1 ' + refs, st[r0 -- i '] = refval(r1), is_array(str, r0, st), st[r0 -- _type] .type ≤ ty, i < st[r0 -- _length] .intval, validrefs(str, acc + r ' + refs0 + r ' + refs1, st[r0 -- _type] .type .type, st), 0 ≤ i, 0 < st[r0 -- _length] .intval, ∀ str, r, refs0, refs1, ty, st. validrefs(str, acc + r ' + refs0 + r ' + refs1, ty, st) ∧ refs1 ≠ [] ∧ refs1 .last = jvmref → validrefs(str, acc + r ' + refs1, ty, st) ⊦ r0 = jvmref, refs1 = [], acc + r ' + refs1 = [] ∨ (∃ i. 0 ≤ i ∧ i < st[r0 -- _length] .intval ∧ is_referencevalue(st[r0 -- i ']) ∧ (acc + r ' + refs1) .first = st[r0 -- i '] .refval ∧ validrefs(str, acc + r ' + refs1, st[r0 -- _type] .type .type, st)), r ≠ r1 ∧ ¬ r ∈ refs, ¬ r1 ∈ acc ∧ r1 ≠ r

Rule argument

[crewrite-arg: validrefs-array , F , [st, ty, refs, r, str] → [st, ty, acc + r ' + refs1, r0, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (st, ty, acc + r ' + refs1, r0, str)]]