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Proof step 25 from proof validrefs-levelsubset (previous step)

st[r -- i '] = refval(r0), 0 ≤ i, 0 < st[r -- _length] .intval, is_array(str0, r, st), is_array(str, r, st), level⊆(str, str0), st[r -- _type] .type ≤ ty0, i < st[r -- _length] .intval, is_referencevalue(st[r -- i ']), validrefs(str, r0 ' + refs, st[r -- _type] .type .type, st), ∀ str1, ty, st0, str2. validrefs(str1, r0 ' + refs, ty, st0) ∧ level⊆(str1, str2) → validrefs(str2, r0 ' + refs, ty, st0) ⊦ r = jvmref, ∃ i0. ¬ i0 < 0 ∧ ¬ st[r -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r -- i0 ']) ∧ r0 = st[r -- i0 '] .refval ∧ validrefs(str0, r0 ' + refs, st[r -- _type] .type .type, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 24:
st[r -- i '] = refval(r0), validrefs(str, r0 ' + refs, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, st[r -- _type] .type ≤ ty0, level⊆(str, str0), is_array(str, r, st), is_array(str0, r, st), 0 < st[r -- _length] .intval, 0 ≤ i, ∀ str1, ty, st0, str2. validrefs(str1, r0 ' + refs, ty, st0) ∧ level⊆(str1, str2) → validrefs(str2, r0 ' + refs, ty, st0) ⊦ r = jvmref, ∃ i0. ¬ i0 < 0 ∧ ¬ st[r -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r -- i0 ']) ∧ r0 = st[r -- i0 '] .refval ∧ validrefs(str0, st[r -- i0 '] .refval ' + refs, st[r -- _type] .type .type, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_referencevalue(refval(r))])]]