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Proof step 181 from proof exvalidrefs-maxlength (previous step)

is_array(str, r0, st) ∧ st[r0 -- _type] .type ≤ mkarraytype(ty), st[r0 -- _type] .type = mkarraytype(ty), st[r0 -- 0 '] = refval(r0), ty .jtelemtype = mkclasstype(`java.lang.Object' .class), 0 < st[r0 -- _length] .intval, junkrefs(str, r0 ' + refs0, (st -- r0)[r0 -- _type] .type, st -- r0), mkarraytype(ty) ≤ ty, is_array(r0, st), is_array(str, r0, st), is_reftype(ty), ∀ r, str, st0. # st0 .refs < # st .refs → ( true → cyclic(str, r, st0) ∨ junkref(str, r, st0) ∨ (∃ refs. validrefs(str, refs, st0[refs .first -- _type] .type, st0) ∧ refs ≠ [] ∧ ¬ dups(refs) ∧ refs .first = r ∧ ¬ has_reffield(refs .last, st0))) ⊦ r0 = jvmref, ty = void_type, junkref(str, r0, st), r0 ' = [] ∨ (∃ i. 0 ≤ i ∧ i < st[r0 -- _length] .intval ∧ is_referencevalue(st[r0 -- i ']) ∧ r0 ' .first = st[r0 -- i '] .refval ∧ validrefs(str, r0 ', st[r0 -- _type] .type .type, st)), ∃ refs. validrefs(str, refs, st[refs .first -- _type] .type, st) ∧ refs ≠ [] ∧ ¬ dups(refs) ∧ refs .first = r0 ∧ ¬ has_reffield(refs .last, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 180:
ty .jtelemtype = mkclasstype(`java.lang.Object' .class), st[r0 -- 0 '] = refval(r0), st[r0 -- _type] .type = mkarraytype(ty), is_reftype(ty), is_array(str, r0, st), is_array(r0, st), mkarraytype(ty) ≤ ty, junkrefs(str, r0 ' + refs0, (st -- r0)[r0 -- _type] .type, st -- r0), 0 < st[r0 -- _length] .intval, ∀ r, str, st0. # st0 .refs < # st .refs → ( true → cyclic(str, r, st0) ∨ junkref(str, r, st0) ∨ (∃ refs. validrefs(str, refs, st0[refs .first -- _type] .type, st0) ∧ refs ≠ [] ∧ ¬ dups(refs) ∧ refs .first = r ∧ ¬ has_reffield(refs .last, st0))) ⊦ ty = void_type, r0 = jvmref, junkref(str, r0, st), ∃ refs. validrefs(str, refs, st[refs .first -- _type] .type, st) ∧ refs ≠ [] ∧ ¬ dups(refs) ∧ refs .first = r0 ∧ ¬ has_reffield(refs .last, st), ∃ i. ¬ i < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i ∧ is_referencevalue(st[r0 -- i ']) ∧ r0 = st[r0 -- i '] .refval ∧ validrefs(str, r0 ', ty, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_arraytype(mkarraytype(ty))], [CSIMPSEQ : ⊦ ty ≤ ty], [CSIMPSEQ : ⊦ mkarraytype(ty) .type = ty], [CSIMPSEQ : ⊦ r ' .first = r], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ ty0 ≤ mkarraytype(ty) ↔ is_arraytype(ty0) ∧ ty0 .type ≤ ty], [CSIMPSEQ : ⊦ r ' ≠ []])]]