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Proof step 163 from proof exvalidrefs-maxlength (previous step)

st[r -- 0 '] = refval(r0), 0 < st[r -- _length] .intval, is_array(str, r, st), is_array(r, st), st[r0 -- _type] .type ≤ st[r -- _type] .type .type, validrefs(str, r0 ' + refs0, (st -- r)[r0 -- _type] .type, st -- r), is_reftype(st[r -- _type] .type .type) ∨ st[r -- _type] .type .type = void_type, ∀ 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))) ⊦ r = jvmref, r0 = jvmref, junkref(str, r0, st), ∃ refs. validrefs(str, refs, st[refs .first -- _type] .type, st) ∧ refs ≠ [] ∧ ¬ dups(refs) ∧ refs .first = r ∧ ¬ has_reffield(refs .last, st), ¬ r0 ∈ refs0 ∧ ¬ dups(refs0), dups(r ' + r0 ' + refs0) ∧ (r ' + r0 ' + refs0) .first = r ∧ validrefs(str, r ' + r0 ' + refs0, st[(r ' + r0 ' + refs0) .first -- _type] .type, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 162:
st[r -- 0 '] = refval(r0), 0 < st[r -- _length] .intval, is_array(str, r, st), is_array(r, st), st[r0 -- _type] .type ≤ st[r -- _type] .type .type, validrefs(str, r0 ' + refs0, (st -- r)[r0 -- _type] .type, st -- r), is_reftype(st[r -- _type] .type .type) ∨ st[r -- _type] .type .type = void_type, ∀ 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))) ⊦ r = jvmref, r0 = jvmref, junkref(str, r0, st), ∃ refs. validrefs(str, refs, st[refs .first -- _type] .type, st) ∧ refs ≠ [] ∧ ¬ dups(refs) ∧ refs .first = r ∧ ¬ has_reffield(refs .last, st), ¬ r0 ∈ refs0 ∧ ¬ dups(refs0), (dups(refs0) ∨ r0 ∈ refs0 ∨ r = r0 ∨ r ∈ refs0) ∧ validrefs(str, r ' + r0 ' + refs0, st[r -- _type] .type, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (r ' + refs) .first = r], [CSIMPSEQ : ⊦ ¬ r ∈ r0 ' + refs ↔ r ≠ r0 ∧ ¬ r ∈ refs], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ dups(r ' + refs) ↔ dups(refs) ∨ r ∈ refs])]]