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Proof step 33 from proof cyclic-addarray-this-01 (previous step)

is_array(str, r0, addarray(r0, ty, vals, st)), newref(r0, st), ∀ r. refval(r) ∈ vals → ¬ junkref(str, r, st) ∧ ¬ cyclic(str, r, st), 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(r0, ty, vals, st)) ⊦ refs0 = [], r0 = jvmref, ¬ r0 ∈ refs0 ∧ ¬ dups(refs0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
refs0 .first = vals[i→n(i)] .refval, 0 ≤ i, validrefs(str, refs0, ty, addarray(r0, ty, vals, st)), is_referencevalue(vals[i→n(i)]), i < n→i(# vals), newref(r0, st), is_array(str, r0, addarray(r0, ty, vals, st)), ∀ r. refval(r) ∈ vals → ¬ junkref(str, r, st) ∧ ¬ cyclic(str, r, st) ⊦ r0 = jvmref, refs0 = [], vals = [], ¬ r0 ∈ 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])]]