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Proof step 51 from proof same-subclasses-array-forward (previous step)

st[r -- i '] = refval(r0), st[r0 -- _type] .type .jtelemtype .class ≤ st[r -- _type] .type .jtelemtype .class, st[r0 -- _type] .type .jtelemtype ≤ st[r -- _type] .type .jtelemtype, is_array(str, r, st), same-subclasses(st[r -- _type] .type .jtelemtype .class, str, str0), i < st[r -- _length] .intval, has_classtype(st[r0 -- _type] .type), 0 ≤ i, 0 < st[r -- _length] .intval, has_classtype(st[r -- _type] .type), contains(str0, st[r0 -- _type] .type .jtelemtype, mkclasstype(class)) ⊦ r0 = jvmref, st[r -- _type] .type .jtelemtype = mkclasstype(`java.lang.Object' .class), junkref(str0, r, st), contains(str0, st[r -- _type] .type .jtelemtype, st[r0 -- _type] .type .jtelemtype), same-subclasses(class, str, str0), contains(str0, st[r -- _type] .type .jtelemtype, mkclasstype(class))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 37:
⊦ contains(str, ty, ty1) ∧ ty ≤ ty0 ∧ type∃(str, ty0) → contains(str, ty0, ty1)
Proof step 50:
¬ ( contains(str0, st[r0 -- _type] .type .jtelemtype, mkclasstype(class)) ∧ st[r0 -- _type] .type .jtelemtype ≤ st[r -- _type] .type .jtelemtype ∧ type∃(str0, st[r -- _type] .type .jtelemtype)), st[r -- i '] = refval(r0), st[r0 -- _type] .type .jtelemtype .class ≤ st[r -- _type] .type .jtelemtype .class, st[r0 -- _type] .type .jtelemtype ≤ st[r -- _type] .type .jtelemtype, is_array(str, r, st), same-subclasses(st[r -- _type] .type .jtelemtype .class, str, str0), i < st[r -- _length] .intval, has_classtype(st[r0 -- _type] .type), 0 ≤ i, 0 < st[r -- _length] .intval, has_classtype(st[r -- _type] .type), contains(str0, st[r0 -- _type] .type .jtelemtype, mkclasstype(class)) ⊦ r0 = jvmref, st[r -- _type] .type .jtelemtype = mkclasstype(`java.lang.Object' .class), junkref(str0, r, st), contains(str0, st[r -- _type] .type .jtelemtype, st[r0 -- _type] .type .jtelemtype), same-subclasses(class, str, str0), contains(str0, st[r -- _type] .type .jtelemtype, mkclasstype(class))

Rule argument

[crewrite-arg: contains-supertype-04 , F , [str, ty, ty1, ty0] → [str0, st[r0 -- _type] .type .jtelemtype, mkclasstype(class), st[r -- _type] .type .jtelemtype] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (str0, st[r0 -- _type] .type .jtelemtype, mkclasstype(class), st[r -- _type] .type .jtelemtype)]]