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Proof step 33 from proof validrefs-append (previous step)

st[r0 -- i '] = refval(r1), acc + r ' = r1 ' + refs, 0 < st[r0 -- _length] .intval, 0 ≤ i, validrefs(str, r1 ' + refs, st[r0 -- _type] .type .type, st), i < st[r0 -- _length] .intval, st[r0 -- _type] .type ≤ ty, validrefs(str, r ' + refs0, ty0, st), is_array(str, r0, st), ∀ str, r, refs0, ty0, st, ty. validrefs(str, r ' + refs0, ty0, st) ∧ validrefs(str, acc + r ', ty, st) → validrefs(str, acc + r ' + refs0, ty, st) ⊦ r0 = jvmref, ¬ r1 ∈ acc ∧ r1 ≠ r, r ≠ r1 ∧ ¬ r ∈ refs, ∃ i0. ¬ i0 < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r0 -- i0 ']) ∧ r1 = st[r0 -- i0 '] .refval ∧ validrefs(str, acc + r ' + refs0, st[r0 -- _type] .type .type, st)

User applied rule exists right

And obtained the following new goals

Proof step 32:
st[r0 -- i '] = refval(r1), acc + r ' = r1 ' + refs, 0 < st[r0 -- _length] .intval, 0 ≤ i, validrefs(str, r1 ' + refs, st[r0 -- _type] .type .type, st), i < st[r0 -- _length] .intval, st[r0 -- _type] .type ≤ ty, validrefs(str, r ' + refs0, ty0, st), is_array(str, r0, st), ∀ str, r, refs0, ty0, st, ty. validrefs(str, r ' + refs0, ty0, st) ∧ validrefs(str, acc + r ', ty, st) → validrefs(str, acc + r ' + refs0, ty, st) ⊦ r0 = jvmref, ¬ r1 ∈ acc ∧ r1 ≠ r, r ≠ r1 ∧ ¬ r ∈ refs, ¬ i < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i ∧ is_referencevalue(st[r0 -- i ']) ∧ r1 = st[r0 -- i '] .refval ∧ validrefs(str, acc + r ' + refs0, st[r0 -- _type] .type .type, st)

Rule argument

[EXRARG : pos: right 4, [extquanttermlist: (i)abort:F, discard:T, computed:T]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (i)]]