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Proof step 44 from proof junkref-addarray-01 (previous step)

vals[i→n(i)] = refval(r0), i < n→i(# vals), class∃(str, class), newref(r, st), is_array(str, r, addarray(r, mkclasstype(class), vals, st)), 0 ≤ i, junkrefs(str, r0 ' + refs, mkclasstype(class), addarray(r, mkclasstype(class), vals, st)), st[r0 -- _type] .type ≤ mkclasstype(class) ⊦ r = jvmref, vals = [], r0 = jvmref, junkrefs(str, r0 ' + refs, st[r0 -- _type] .type, st), ∃ refs0. refs0 ≠ [] ∧ refs0 .first = r0 ∧ junkrefs(str, refs0, st[refs0 .first -- _type] .type, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 42:
⊦ ¬ junkrefs(str, refs, ty, st) ∧ newref(r0, st) → ¬ junkrefs(str, refs, ty, addarray(r0, ty0, vals, st))
Proof step 43:
⊦ ¬ junkrefs(str, r ' + refs, st[r -- _type] .type, st) ∧ r ≠ jvmref → (junkrefs(str, r ' + refs, ty, st) ↔ ¬ st[r -- _type] .type ≤ ty)

Rule argument

[crewrite-arg: junkrefs-addarray , F , [st, vals, ty0, r0, ty, refs, str] → [st, vals, mkclasstype(class), r, mkclasstype(class), r0 ' + refs, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (st, vals, mkclasstype(class), r, mkclasstype(class), r0 ' + refs, str)]]