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Proof step 20 from proof cyclic-addrefarray (previous step)

vals[i→n(i)] = refval(r0), refval(r0) ∈ vals, 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, r0 ' + 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), r0 ≠ jvmref → st[r0 -- _type] .type ≤ ty ⊦ r = jvmref, ty .jtelemtype = void_type, ty .jtelemtype = abstract_type, vals = [], r = r0, cyclic(str, r0, st), junkref(str, r0, st), ¬ dups(refs) ∧ ¬ r0 ∈ refs ∧ ¬ r ∈ refs

User applied rule cut formula

And obtained the following new goals

Proof step 17:
r0 ≠ jvmref, vals[i→n(i)] = refval(r0), refval(r0) ∈ vals, 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, r0 ' + 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), r0 ≠ jvmref → st[r0 -- _type] .type ≤ ty ⊦ r = jvmref, ty .jtelemtype = void_type, ty .jtelemtype = abstract_type, vals = [], r = r0, cyclic(str, r0, st), junkref(str, r0, st), ¬ dups(refs) ∧ ¬ r0 ∈ refs ∧ ¬ r ∈ refs
Proof step 18:
⊦ validrefs(str, jvmref ' + refs, ty, st) ↔ refs = []
Proof step 19:
⊦ ¬ cyclic(str, jvmref, st)

Rule argument

[fma-arg: r0 ≠ jvmref]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ ¬ junkref(str, jvmref, st)], [CSIMPSEQ : ⊦ ¬ dups([])], [CSIMPSEQ : ⊦ ¬ r ∈ []])], [EXTRAFMAS : (r0 ≠ jvmref)]]