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Proof step 49 from proof junkref-subspec-samesubclasses (previous step)

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)) ⊦ ¬ has_classtype(st[r0 -- _type] .type) ∧ junkref(str, r0, st), 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)

User applied rule case distinction

And closed the goal!

Rule argument

[CASEDARG : pos: right 1, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ junkref(str, r, st) → ( junkrefs (str, r ' + refs0, st[r -- _type] .type, st) ↔ false)], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]