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Proof step 36 from proof cyclic-addrefarray (previous step)

newref(r, st), type∃(str, ty), is_reftype(ty), is_array(str, r, 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), refs0 = [] ∨ 0 ≤ i ∧ i < n→i(# vals) ∧ is_referencevalue(vals[i→n(i)]) ∧ refs0 .first = vals[i→n(i)] .refval ∧ validrefs(str, refs0, ty, addarray(r, ty, vals, st)) ⊦ refs0 = [], ty .jtelemtype = abstract_type, ty .jtelemtype = void_type, r = jvmref, ¬ r ∈ refs0 ∧ ¬ dups(refs0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 35:
refs0 .first = 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)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ # vals = 0 ↔ vals = []], [CSIMPSEQ : ⊦ 0 < n ↔ n ≠ 0], [CSIMPSEQ : 0 ≤ i ⊦ ((* i)) < n→i(n) ↔ i→n(i) < n], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j])]]