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Proof step 22 from proof same-subclasses-array-forward (previous step)

is_array(str0, r, st), st[r -- i '] = refval(r0), st[r -- _type] .type = mkarraytype(ty), 0 < st[r -- _length] .intval, 0 ≤ i, has_classtype(st[r0 -- _type] .type), i < st[r -- _length] .intval, is_array(str0, r, st), same-subclasses(ty .jtelemtype .class, str, str0), is_array(str, r, st), has_classtype(ty), ∀ class0. contains(str0, ty .jtelemtype, mkclasstype(class0)) → same-subclasses(class0, str, str0) ⊦ ty .jtelemtype = mkclasstype(`java.lang.Object' .class), r0 = jvmref, r = jvmref, st[r0 -- _type] .type .jtelemtype ≤ ty .jtelemtype, contains(str0, ty .jtelemtype, st[r0 -- _type] .type .jtelemtype), ∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ st[r -- i '] .refval ≠ jvmref ∧ (¬ st[st[r -- i '] .refval -- _type] .type ≤ st[r -- _type] .type .type ∨ junkref(str0, st[r -- i '] .refval, st)), contains(str0, mkarraytype(ty), st[r0 -- _type] .type), same-subclasses(st[r0 -- _type] .type .jtelemtype .class, str, str0) ∧ (contains(str0, st[r0 -- _type] .type .jtelemtype, mkclasstype(class)) → same-subclasses(class, str, str0))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
st[r -- _type] .type = mkarraytype(ty), st[r -- i '] = refval(r0), has_classtype(ty), is_array(str, r, st), same-subclasses(ty .jtelemtype .class, str, str0), is_array(str0, r, st), i < st[r -- _length] .intval, has_classtype(st[r0 -- _type] .type), 0 ≤ i, 0 < st[r -- _length] .intval, ∀ class0. contains(str0, ty .jtelemtype, mkclasstype(class0)) → same-subclasses(class0, str, str0) ⊦ r = jvmref, r0 = jvmref, ty .jtelemtype = mkclasstype(`java.lang.Object' .class), contains(str0, mkarraytype(ty), st[r0 -- _type] .type), contains(str0, ty .jtelemtype, st[r0 -- _type] .type .jtelemtype), st[r0 -- _type] .type .jtelemtype ≤ ty .jtelemtype, same-subclasses(st[r0 -- _type] .type .jtelemtype .class, str, str0) ∧ (contains(str0, st[r0 -- _type] .type .jtelemtype, mkclasstype(class)) → same-subclasses(class, str, str0)), ∃ i0. ¬ i0 < 0 ∧ ¬ st[r -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r -- i0 ']) ∧ st[r -- i0 '] .refval ≠ jvmref ∧ (¬ st[st[r -- i0 '] .refval -- _type] .type ≤ ty ∨ junkref(str0, st[r -- i0 '] .refval, st))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ mkarraytype(ty) .type = ty], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i])]]