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Proof step 30 from proof junkref-primarray-level-01 (previous step)

junkrefs(str, r ' + refs0, st[r -- _type] .type, st), is_array(str1, r, st), ∀ str1, st, r, str, refs. # refs < # refs0 → (junkrefs(str, r ' + refs, st[r -- _type] .type, st) → has_classtype(st[r -- _type] .type) ∨ junkrefs(str1, r ' + refs, st[r -- _type] .type, st)) ⊦ r = jvmref, junkrefs(str1, r ' + refs0, st[r -- _type] .type, st), has_classtype(st[r -- _type] .type)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( junkrefs(str, r ' + refs, ty, st) ↔ refs ≠ [] ∧ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ refs .first = st[r -- i '] .refval ∧ junkrefs(str, refs, st[r -- _type] .type .type, st)))
Proof step 29:
is_array(str, r, st) ∧ st[r -- _type] .type ≤ st[r -- _type] .type, refs0 ≠ [] ∧ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ refs0 .first = st[r -- i '] .refval ∧ junkrefs(str, refs0, st[r -- _type] .type .type, st)), is_array(str1, r, st), ∀ str1, st, r, str, refs. # refs < # refs0 → (junkrefs(str, r ' + refs, st[r -- _type] .type, st) → has_classtype(st[r -- _type] .type) ∨ junkrefs(str1, r ' + refs, st[r -- _type] .type, st)) ⊦ r = jvmref, junkrefs(str1, r ' + refs0, st[r -- _type] .type, st), has_classtype(st[r -- _type] .type)

Rule argument

[crewrite-arg: junkrefs-array , F , [st, ty, refs, r, str] → [st, st[r -- _type] .type, refs0, r, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ has_classtype(ty) → (ty0 ≤ ty ↔ ty0 = ty)], [CSIMPSEQ : ⊦ ¬ is_array(str, r, st) ∧ ¬ has_classtype (st[r -- _type] .type) → ¬ is_array(str0, r, st)])], [EXTRATERMS : (st, st[r -- _type] .type, refs0, r, str)]]