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Proof step 41 from proof validrefs-put-notin (previous step)

st[r0 -- i '] = refval(r1), is_referencevalue(st[r0 -- i ']), validrefs(str, r1 ' + refs, st[r0 -- _type] .type .type, st), is_array(str, r0, st), st[r0 -- _type] .type ≤ ty, i < st[r0 -- _length] .intval, 0 ≤ i, 0 < st[r0 -- _length] .intval, ∀ 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, r = r1, r ∈ refs, ∃ i0. ¬ i0 < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r0 -- i0 ']) ∧ r1 = st[r0 -- i0 '] .refval ∧ validrefs(str, st[r0 -- i0 '] .refval ' + refs, st[r0 -- _type] .type .type, st[r -- sk, val])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 40:
st[r0 -- i '] = refval(r1), 0 < st[r0 -- _length] .intval, 0 ≤ i, i < st[r0 -- _length] .intval, st[r0 -- _type] .type ≤ ty, is_array(str, r0, st), validrefs(str, r1 ' + refs, st[r0 -- _type] .type .type, st), ∀ 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 ⊦ r = r1, r = r0, r0 = jvmref, r ∈ refs, ∃ i0. ¬ i0 < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r0 -- i0 ']) ∧ r1 = st[r0 -- i0 '] .refval ∧ validrefs(str, st[r0 -- i0 '] .refval ' + refs, st[r0 -- _type] .type .type, st[r -- sk, val])

Rule argument

[emptyarg]

Additional information

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