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Proof step 52 from proof junkref-subspec-samesubclasses (previous step)

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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 51:
st[r -- i '] = refval(r0), st[r -- _type] .type = mkarraytype(ty), is_array(str0, r, st), junkrefs(str, r0 ' + refs1, st[r0 -- _type] .type, st), st[r0 -- _type] .type ≤ ty, i < st[r -- _length] .intval, same-subclasses-contains(ty .jtelemtype .class, str, str0), is_array(str, r, st), 0 < st[r -- _length] .intval, 0 ≤ i, has_classtype(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)) ⊦ r = jvmref, r0 = jvmref, junkref(str0, r0, st), same-subclasses-contains(st[r0 -- _type] .type .jtelemtype .class, str, str0), has_classtype(st[r0 -- _type] .type)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_arraytype(mkarraytype(ty))], [CSIMPSEQ : ⊦ has_classtype(mkarraytype(ty)) ↔ has_classtype(ty)], [CSIMPSEQ : ⊦ mkarraytype(ty) .type = ty], [CSIMPSEQ : ⊦ is_arraytype(ty) → ty .jtelemtype = ty .type .jtelemtype])]]