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Proof step 242 from proof exvalidrefs-maxlength (previous step)

is_array(str, r, st) ∧ st[r -- _type] .type ≤ st[r -- _type] .type, st[r -- 0 '] = refval(r0), validrefs(str, r0 ' + refs1 + r1 ', st[r0 -- _type] .type, st -- r), st[r0 -- _type] .type ≤ st[r -- _type] .type .type, is_array(r, st), is_array(str, r, st), 0 < st[r -- _length] .intval, validrefs(str, r0 ' + refs1 + r1 ', st[r0 -- _type] .type, st), 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))) ⊦ r0 = r1, r = r1, r = r0, r0 = jvmref, r = jvmref, r0 ∈ refs1, dups(refs1), r1 ∈ refs1, has_reffield(r1, st), junkref(str, r0, st), cyclic(str, r, st), r ∈ refs1, r0 ' + refs1 + r1 ' = [] ∨ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ (r0 ' + refs1 + r1 ') .first = st[r -- i '] .refval ∧ validrefs(str, r0 ' + refs1 + r1 ', st[r -- _type] .type .type, st))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 241:
st[r -- 0 '] = refval(r0), validrefs(str, r0 ' + refs1 + r1 ', st[r0 -- _type] .type, st -- r), st[r0 -- _type] .type ≤ st[r -- _type] .type .type, is_array(r, st), is_array(str, r, st), 0 < st[r -- _length] .intval, validrefs(str, r0 ' + refs1 + r1 ', st[r0 -- _type] .type, st), 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))) ⊦ r0 = r1, r = r1, r = r0, r0 = jvmref, r = jvmref, r0 ∈ refs1, dups(refs1), r1 ∈ refs1, has_reffield(r1, st), junkref(str, r0, st), cyclic(str, r, st), r ∈ refs1, ∃ i. ¬ i < 0 ∧ ¬ st[r -- _length] .intval ≤ i ∧ is_referencevalue(st[r -- i ']) ∧ r0 = st[r -- i '] .refval ∧ validrefs(str, st[r -- i '] .refval ' + refs1 + r1 ', st[r -- _type] .type .type, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (r ' + refs) .first = r], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ ty ≤ ty], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' + refs ≠ []])]]