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Proof step 35 from proof cyclic-addarray-this-01 (previous step)

is_array(str, r0, addarray(r0, ty, vals, st)) ∧ (addarray(r0, ty, vals, st)[r0 -- _type]) .type ≤ mkarraytype(ty), newref(r0, st), refs0 = [] ∨ (∃ i. 0 ≤ i ∧ i < (addarray(r0, ty, vals, st)[r0 -- _length]) .intval ∧ is_referencevalue(addarray(r0, ty, vals, st)[r0 -- i ']) ∧ refs0 .first = (addarray(r0, ty, vals, st)[r0 -- i ']) .refval ∧ validrefs(str, refs0, (addarray(r0, ty, vals, st)[r0 -- _type]) .type .type, addarray(r0, ty, vals, st))), is_valid_ref(str, r0, addarray(r0, ty, vals, st)), ∀ r. refval(r) ∈ vals → ¬ junkref(str, r, st) ∧ ¬ cyclic(str, r, st) ⊦ r0 = jvmref, ¬ r0 ∈ refs0 ∧ ¬ dups(refs0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 34:
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)) ⊦ r0 = jvmref, ¬ r0 ∈ refs0 ∧ ¬ dups(refs0)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ mkarraytype(ty) .type = ty], [CSIMPSEQ : ⊦ 0 ≤ i ∧ i < n→i(# vals) → (addarray(r, ty, vals, st) [r -- i ' ] ) = vals[i→n(i)]], [CSIMPSEQ : ⊦ intval(i) .intval = i], [CSIMPSEQ : ⊦ (addarray(r, ty, vals, st) [r -- _length ] ) = intval(n→i(# vals))], [CSIMPSEQ : ⊦ is_array(str, r, st) → is_valid_ref(str, r, st)], [CSIMPSEQ : ⊦ ty ≤ ty], [CSIMPSEQ : ⊦ mkarraytype(ty) ≤ mkarraytype(ty0) ↔ ty ≤ ty0], [CSIMPSEQ : ⊦ typeval(ty) .type = ty], [CSIMPSEQ : ⊦ (addarray(r, ty, vals, st) [r -- _type ] ) = typeval(mkarraytype(ty))])]]