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Proof step 44 from proof validrefs-put-statfield (previous step)

is_array(str, r, st), st[r -- _type] .type ≤ ty, ∀ str0, ty0, st0, sk0, val0. validrefs(str0, r0 ' + refs, ty0, st0[jvmref -- sk0, val0]) ↔ validrefs(str0, r0 ' + refs, ty0, st0) ⊦ r = jvmref, (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ r0 = st[r -- i '] .refval ∧ validrefs(str, st[r -- i '] .refval ' + refs, st[r -- _type] .type .type, st[jvmref -- sk, val])) ↔ (∃ i. ¬ i < 0 ∧ ¬ st[r -- _length] .intval ≤ i ∧ is_referencevalue(st[r -- i ']) ∧ r0 = st[r -- i '] .refval ∧ validrefs(str, st[r -- i '] .refval ' + refs, st[r -- _type] .type .type, st))

User applied rule case distinction

And obtained the following new goals

Rule argument

[CASEDARG : pos: right 2, ()]

Additional information

[[CONCRETESIMPRULES : ()]]