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Proof step 31 from proof junkref-addarray-04 (previous step)

is_array(str, r, addarray(r, ty, vals, st)), ∃ i. 0 ≤ i ∧ i < (addarray(r, ty, vals, st)[r -- _length]) .intval ∧ is_referencevalue(addarray(r, ty, vals, st)[r -- i ']) ∧ (addarray(r, ty, vals, st)[r -- i ']) .refval ≠ jvmref ∧ ( ¬ (addarray(r, ty, vals, st)[(addarray(r, ty, vals, st)[r -- i ']) .refval -- _type]) .type ≤ (addarray(r, ty, vals, st)[r -- _type]) .type .type ∨ junkref(str, (addarray(r, ty, vals, st)[r -- i ']) .refval, addarray(r, ty, vals, st))), validreflist(str, vals, ty, st), newref(r, st), type∃(str, ty), is_reftype(ty) ⊦ ty .jtelemtype = void_type, ty .jtelemtype = abstract_type, r = jvmref

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 30:
0 ≤ i, 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), validreflist(str, vals, ty, st), ¬ (addarray(r, ty, vals, st)[vals[i→n(i)] .refval -- _type]) .type ≤ ty ∨ junkref(str, vals[i→n(i)] .refval, addarray(r, ty, vals, st)) ⊦ vals[i→n(i)] .refval = jvmref, r = jvmref, ty .jtelemtype = abstract_type, ty .jtelemtype = void_type, vals = []

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], [CSIMPSEQ : ⊦ mkarraytype(ty) .type = ty], [CSIMPSEQ : ⊦ typeval(ty) .type = ty], [CSIMPSEQ : ⊦ (addarray(r, ty, vals, st) [r -- _type ] ) = typeval(mkarraytype(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))])]]