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Proof step 19 from proof junkref-primarray-level-01 (previous step)

st[r -- i '] = refval(r0), is_array(str1, r, st), 0 ≤ i, 0 < st[r -- _length] .intval, is_array(str, r, st), i < st[r -- _length] .intval, junkrefs(str, r0 ' + refs1, st[r -- _type] .type .type, st), ∀ str1, st0, r1, str, refs. # refs < # (r0 + refs1) → ( junkrefs(str, r1 ' + refs, st0[r1 -- _type] .type, st0) → has_classtype(st0[r1 -- _type] .type) ∨ junkrefs(str1, r1 ' + refs, st0[r1 -- _type] .type, st0)) ⊦ st[r -- _type] .type .type = st[r0 -- _type] .type, r = jvmref, has_classtype(st[r -- _type] .type), junkrefs(str1, r0 ' + refs1, st[r -- _type] .type .type, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ r ≠ jvmref ∧ (¬ is_valid_ref(str, r, st) ∨ ¬ st[r -- _type] .type ≤ ty) → junkrefs(str, r ' + refs, ty, st)
Proof step 18:
¬ (r0 ≠ jvmref ∧ (¬ is_valid_ref(str1, r0, st) ∨ ¬ st[r0 -- _type] .type ≤ st[r -- _type] .type .type)), st[r -- i '] = refval(r0), is_array(str1, r, st), 0 ≤ i, 0 < st[r -- _length] .intval, is_array(str, r, st), i < st[r -- _length] .intval, junkrefs(str, r0 ' + refs1, st[r -- _type] .type .type, st), ∀ str1, st0, r1, str, refs. # refs < # (r0 + refs1) → ( junkrefs(str, r1 ' + refs, st0[r1 -- _type] .type, st0) → has_classtype(st0[r1 -- _type] .type) ∨ junkrefs(str1, r1 ' + refs, st0[r1 -- _type] .type, st0)) ⊦ st[r -- _type] .type .type = st[r0 -- _type] .type, r = jvmref, has_classtype(st[r -- _type] .type), junkrefs(str1, r0 ' + refs1, st[r -- _type] .type .type, st)

Rule argument

[crewrite-arg: junkrefs-is-junk , F , [st, ty, refs, r, str] → [st, st[r -- _type] .type .type, refs1, r0, str1] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, st[r -- _type] .type .type, refs1, r0, str1)]]