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Proof step 48 from proof unchNorec-validrefs (previous step)

st0[r -- _type] .type = mkarraytype(ty0), st[r -- _type] = st0[r -- _type], st[r -- _length] = st0[r -- _length], is_array(str, r, st), st0[r -- _type] .type ≤ ty, unchangedNorec(r, st, st0), is_arraytype(st0[r -- _type] .type), ∀ r0. r0 ∈ refs0 → unchangedNorec(r0, st, st0), refs0 = [] ∨ 0 ≤ i ∧ i < st0[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ refs0 .first = st[r -- i '] .refval ∧ validrefs(str, refs0, ty0, st), ∀ str, ty, st, st0. validrefs(str, refs0, ty, st) ∧ (∀ r. r ∈ refs0 → unchangedNorec(r, st, st0)) → validrefs(str, refs0, ty, st0) ⊦ r = jvmref, validrefs(str, r ' + refs0, ty, st0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 47:
st[r -- _length] = st0[r -- _length], st[r -- _type] = st0[r -- _type], st0[r -- _type] .type = mkarraytype(ty0), unchangedNorec(r, st, st0), mkarraytype(ty0) ≤ ty, is_array(str, r, st), ∀ str, ty, st, st0. validrefs(str, refs0, ty, st) ∧ (∀ r. r ∈ refs0 → unchangedNorec(r, st, st0)) → validrefs(str, refs0, ty, st0), refs0 = [] ∨ 0 ≤ i ∧ i < st0[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ refs0 .first = st[r -- i '] .refval ∧ validrefs(str, refs0, ty0, st), ∀ r0. r0 ∈ refs0 → unchangedNorec(r0, st, st0) ⊦ r = jvmref, validrefs(str, r ' + refs0, ty, st0)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_arraytype(mkarraytype(ty))])]]