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Proof step 84 from proof same-subclasses-array-forward (previous step)

st[r -- _type] .type = mkarraytype(ty), st[r -- i '] = refval(r0), ty .jtelemtype = mkclasstype(`java.lang.Object' .class), st[r0 -- _type] .type = mkarraytype(ty0), i < st[r -- _length] .intval, same-subclasses(`java.lang.Object' .class, str, str0), is_array(str, r, st), has_classtype(ty), 0 < st[r -- _length] .intval, 0 ≤ i, has_classtype(ty0), ∀ class0. contains(str0, mkclasstype(`java.lang.Object' .class), mkclasstype(class0)) → same-subclasses(class0, str, str0) ⊦ r0 = jvmref, type∃(str0, mkclasstype(`java.lang.Object' .class)) ∧ is_reftype(mkclasstype(`java.lang.Object' .class)) ∧ ( (∃ ty1. ty1 ≤ mkclasstype(`java.lang.Object' .class) ∧ type∃(str0, ty1) ∧ type∃(str0, ty0 .jtelemtype) ∧ (is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty0 .jtelemtype ≤ fs .type)) ∧ (is_arraytype(ty1) → ty0 .jtelemtype ≤ ty1 .type)) ∨ (∃ ty1, ty2. ty1 ≤ mkclasstype(`java.lang.Object' .class) ∧ type∃(str0, ty1) ∧ (is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty2 ≤ fs .type)) ∧ (is_arraytype(ty1) → ty2 ≤ ty1 .type) ∧ contains(str0, ty2, ty0 .jtelemtype))), junkref(str0, r, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 83:
st[r -- _type] .type = mkarraytype(ty), st[r -- i '] = refval(r0), ty .jtelemtype = mkclasstype(`java.lang.Object' .class), st[r0 -- _type] .type = mkarraytype(ty0), i < st[r -- _length] .intval, same-subclasses(`java.lang.Object' .class, str, str0), is_array(str, r, st), has_classtype(ty), 0 < st[r -- _length] .intval, 0 ≤ i, has_classtype(ty0), ∀ class0. contains(str0, mkclasstype(`java.lang.Object' .class), mkclasstype(class0)) → same-subclasses(class0, str, str0) ⊦ r0 = jvmref, junkref(str0, r, st), ∃ ty1. (is_classtype(ty1) ∨ is_arraytype(ty1)) ∧ type∃(str0, ty1) ∧ type∃(str0, ty0 .jtelemtype) ∧ (is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty0 .jtelemtype ≤ fs .type)) ∧ (is_arraytype(ty1) → ty0 .jtelemtype ≤ ty1 .type), ∃ ty1, ty2. (is_classtype(ty1) ∨ is_arraytype(ty1)) ∧ type∃(str0, ty1) ∧ (is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty2 ≤ fs .type)) ∧ (is_arraytype(ty1) → ty2 ≤ ty1 .type) ∧ contains(str0, ty2, ty0 .jtelemtype)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ type∃(str, ty) → ( ty ≤ mkclasstype (`java.lang.Object' .class) ↔ is_classtype(ty) ∨ is_arraytype(ty))], [CSIMPSEQ : ⊦ is_reftype(mkclasstype(class))], [CSIMPSEQ : ⊦ tdname+∃ (str, `java.lang.Object' .class)], [CSIMPSEQ : ⊦ type∃(str, mkclasstype(class)) ↔ tdname+∃(str, class)])]]