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Proof step 53 from proof junkref-subspec-samesubclasses (previous step)

st[r -- i '] = refval(r0), junkrefs(str, r0 ' + refs1, st[r0 -- _type] .type, st), is_array(str0, r, st), has_classtype(st[r -- _type] .type), 0 ≤ i, 0 < st[r -- _length] .intval, is_array(str, r, st), same-subclasses-contains(st[r -- _type] .type .jtelemtype .class, str, str0), i < st[r -- _length] .intval, st[r0 -- _type] .type ≤ st[r -- _type] .type .type, ∀ str0, str, r1, st0, refs. # refs < # (r0 + refs1) → ( same-subclasses-contains(st0[r1 -- _type] .type .jtelemtype .class, str, str0) ∧ junkrefs(str, r1 ' + refs, st0[r1 -- _type] .type, st0) → junkref(str0, r1, st0)) ⊦ r0 = jvmref, r = jvmref, has_classtype(st[r0 -- _type] .type), same-subclasses-contains(st[r0 -- _type] .type .jtelemtype .class, str, str0), junkref(str0, r0, st)

User applied rule insert elim lemma

And obtained the following new goals

Proof step 52:
st[r -- _type] .type = mkarraytype(ty) ∧ is_arraytype(st[r -- _type] .type), st[r -- i '] = refval(r0), junkrefs(str, r0 ' + refs1, st[r0 -- _type] .type, st), is_array(str0, r, st), has_classtype(st[r -- _type] .type), 0 ≤ i, 0 < st[r -- _length] .intval, is_array(str, r, st), same-subclasses-contains(st[r -- _type] .type .jtelemtype .class, str, str0), i < st[r -- _length] .intval, st[r0 -- _type] .type ≤ ty, ∀ str0, str, r1, st0, refs. # refs < # (r0 + refs1) → ( same-subclasses-contains(st0[r1 -- _type] .type .jtelemtype .class, str, str0) ∧ junkrefs(str, r1 ' + refs, st0[r1 -- _type] .type, st0) → junkref(str0, r1, st0)) ⊦ r0 = jvmref, r = jvmref, has_classtype(st[r0 -- _type] .type), same-subclasses-contains(st[r0 -- _type] .type .jtelemtype .class, str, str0), junkref(str0, r0, st)

Rule argument

[speclemmaarg: ,is_arraytype(ty) → (ty0 = ty .type ↔ ty = mkarraytype(ty0)) ,[ty, ty0] → [st[r -- _type] .type, ty] ,T ,javatype , ,elim-01 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_arraytype (st[r -- _type] .type) → ¬ is_array(str, r, st)], [CSIMPELIM : ⊦ is_arraytype(ty) → ( ty0 = ty .type ↔ ty = mkarraytype(ty0))])], [EXTRATERMS : (st[r -- _type] .type, ty)]]