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Proof step 31 from proof validrefs-contains-null (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 24:
⊦ 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 30:
is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty, acc + jvmref ' = r0 ' + refs, st[r -- i '] = refval(r0), is_array(str, r, st), st[r -- _type] .type ≤ ty, i < st[r -- _length] .intval, validrefs(str, acc + jvmref ' + refs0, st[r -- _type] .type .type, st), 0 ≤ i, 0 < st[r -- _length] .intval, ∀ str, refs0, ty, st. validrefs(str, acc + jvmref ' + refs0, ty, st) → validrefs(str, r0 ' + refs, ty, st) ∧ refs0 = [] ⊦ r = jvmref, ( acc + jvmref ' = [] ∨ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ (acc + jvmref ') .first = st[r -- i '] .refval ∧ validrefs(str, acc + jvmref ', st[r -- _type] .type .type, st))) ∧ refs0 = [], jvmref ≠ r0 ∧ ¬ jvmref ∈ refs, ¬ r0 ∈ acc ∧ r0 ≠ jvmref

Rule argument

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

Additional information

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