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Proof step 73 from proof junkrefs-union-disjoint (previous step)

st1 .refs ∩ st .refs = ∅, is_array(str, r, st1), junkrefs(str, r ' + r0 ' + acc, ty, st1 ∪ st), r ∈ st1, st1[r -- _type] .type ≤ ty, ∀ st1, st, r, str, ty. st1 .refs ∩ st .refs = ∅ ∧ r ∈ st1 ∧ junkrefs(str, r ' + acc, ty, st1 ∪ st) → junkrefs(str, r ' + acc, ty, st1) ⊦ r = jvmref, (st1 ∪ st)[r -- _type] .type ≤ ty, ∃ i. ¬ i < 0 ∧ ¬ st1[r -- _length] .intval ≤ i ∧ is_referencevalue(st1[r -- i ']) ∧ r0 = st1[r -- i '] .refval ∧ junkrefs(str, st1[r -- i '] .refval ' + acc, st1[r -- _type] .type .type, st1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 66:
⊦ ¬ rk ∈ st0 → (st ∪ st0)[rk] = st[rk]
Proof step 72:
¬ ¬ r -- _type ∈ st, st1 .refs ∩ st .refs = ∅, is_array(str, r, st1), junkrefs(str, r ' + r0 ' + acc, ty, st1 ∪ st), r ∈ st1, st1[r -- _type] .type ≤ ty, ∀ st1, st, r, str, ty. st1 .refs ∩ st .refs = ∅ ∧ r ∈ st1 ∧ junkrefs(str, r ' + acc, ty, st1 ∪ st) → junkrefs(str, r ' + acc, ty, st1) ⊦ r = jvmref, (st1 ∪ st)[r -- _type] .type ≤ ty, ∃ i. ¬ i < 0 ∧ ¬ st1[r -- _length] .intval ≤ i ∧ is_referencevalue(st1[r -- i ']) ∧ r0 = st1[r -- i '] .refval ∧ junkrefs(str, st1[r -- i '] .refval ' + acc, st1[r -- _type] .type .type, st1)

Rule argument

[speclemmaarg: ,¬ rk ∈ st0 → (st ∪ st0)[rk] = st[rk] ,[rk, st0, st] → [r -- _type, st, st1] ,F ,storefunsx , ,union-at-left ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (r -- _type, st, st1)]]