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

is_array(str, r0, st), st[r0 -- _type] .type ≤ ty, ∀ str0, ty0, st0, r2, sk0, val0. (validrefs(str0, r1 ' + refs, ty0, st0[r2 -- sk0, val0]) ↔ validrefs(str0, r1 ' + refs, ty0, st0)) ∨ r2 = r1 ∨ r2 ∈ refs ⊦ r0 = jvmref, r = r0, (∃ i. 0 ≤ i ∧ i < st[r0 -- _length] .intval ∧ is_referencevalue(st[r0 -- i ']) ∧ r1 = st[r0 -- i '] .refval ∧ validrefs(str, st[r0 -- i '] .refval ' + refs, st[r0 -- _type] .type .type, st[r -- sk, val])) ↔ (∃ i. ¬ i < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i ∧ is_referencevalue(st[r0 -- i ']) ∧ r1 = st[r0 -- i '] .refval ∧ validrefs(str, st[r0 -- i '] .refval ' + refs, st[r0 -- _type] .type .type, st)), r = r1, r ∈ refs

User applied rule case distinction

And obtained the following new goals

Rule argument

[CASEDARG : pos: right 3, ()]

Additional information

[[CONCRETESIMPRULES : ()]]