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Proof step 34 from proof cyclic-addrefarray (previous step)

refs0 = r0 + refs, r0 = vals[i→n(i)] .refval, 0 ≤ i, validrefs(str, refs0, ty, addarray(r, ty, vals, st)), is_referencevalue(vals[i→n(i)]), i < n→i(# vals), is_array(str, r, addarray(r, ty, vals, st)), is_reftype(ty), type∃(str, ty), newref(r, st), ∀ val. val ∈ vals → ¬ junkref(str, val .refval, st) ∧ ¬ cyclic(str, val .refval, st) ∧ is_referencevalue(val) ∧ (val .refval ≠ jvmref → st[val .refval -- _type] .type ≤ ty) ⊦ r = jvmref, ty .jtelemtype = void_type, ty .jtelemtype = abstract_type, refs0 = [], vals = [], ¬ r ∈ refs0 ∧ ¬ dups(refs0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 33:
is_referencevalue(vals[i→n(i)]), i < n→i(# vals), is_array(str, r, addarray(r, ty, vals, st)), is_reftype(ty), type∃(str, ty), newref(r, st), 0 ≤ i, validrefs(str, vals[i→n(i)] .refval ' + refs, ty, addarray(r, ty, vals, st)), ∀ val. val ∈ vals → ¬ junkref(str, val .refval, st) ∧ ¬ cyclic(str, val .refval, st) ∧ is_referencevalue(val) ∧ (val .refval ≠ jvmref → st[val .refval -- _type] .type ≤ ty) ⊦ r = jvmref, ty .jtelemtype = void_type, ty .jtelemtype = abstract_type, vals = [], r ≠ vals[i→n(i)] .refval ∧ ¬ r ∈ refs ∧ ¬ vals[i→n(i)] .refval ∈ refs ∧ ¬ dups(refs)

Rule argument

[emptyarg]

Additional information

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