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Proof step 10 from proof cyclic-def-simple (previous step)

refs1 = r0 + refs, r0 = st[r -- i '] .refval, is_array(str, r, st), i < st[r -- _length] .intval, is_referencevalue(st[r -- i ']), validrefs(str, refs1, st[r -- _type] .type .type, st), 0 ≤ i, 0 < st[r -- _length] .intval, dups(refs1) ∨ r ∈ refs1 ⊦ r = jvmref, refs1 = [], ¬ r ∈ refs1 ∧ ¬ dups(refs1), ∃ i0. ¬ i0 < 0 ∧ ¬ st[r -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r -- i0 ']) ∧ r0 = st[r -- i0 '] .refval

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
0 ≤ i, 0 < st[r -- _length] .intval, is_array(str, r, st), i < st[r -- _length] .intval, is_referencevalue(st[r -- i ']), validrefs(str, st[r -- i '] .refval ' + refs, st[r -- _type] .type .type, st), st[r -- i '] .refval ∈ refs ∨ dups(refs) ∨ r = st[r -- i '] .refval ∨ r ∈ refs ⊦ r = jvmref, ∃ i0. ¬ i0 < 0 ∧ ¬ st[r -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r -- i0 ']) ∧ st[r -- i '] .refval = st[r -- i0 '] .refval, r ≠ st[r -- i '] .refval ∧ ¬ r ∈ refs ∧ ¬ st[r -- i '] .refval ∈ refs ∧ ¬ dups(refs)

Rule argument

[emptyarg]

Additional information

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