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Proof step 35 from proof junkrefs-subset (previous step)

is_array(str, r, st), junkrefs(str, r ' + acc, ty, st1), st ⊆ st1, st[r -- _type] .type ≤ ty, ∀ str, ty, st1, st. junkrefs(str, acc, ty, st1) ∧ st ⊆ st1 → junkrefs(str, acc, ty, st) ⊦ r = jvmref, st1[r -- _type] .type ≤ ty, acc ≠ [] ∧ (∃ i. ¬ i < 0 ∧ ¬ st[r -- _length] .intval ≤ i ∧ is_referencevalue(st[r -- i ']) ∧ acc .first = st[r -- i '] .refval ∧ junkrefs(str, acc, st[r -- _type] .type .type, st))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 33:
⊦ st1 ⊆ st2 ↔ (∀ rk. rk ∈ st1 → rk ∈ st2 ∧ st1[rk] = st2[rk])
Proof step 34:
is_array(str, r, st), junkrefs(str, r ' + acc, ty, st1), ∀ rk. rk ∈ st → rk ∈ st1 ∧ st[rk] = st1[rk], st[r -- _type] .type ≤ ty, ∀ str, ty, st1, st. junkrefs(str, acc, ty, st1) ∧ st ⊆ st1 → junkrefs(str, acc, ty, st) ⊦ r = jvmref, st1[r -- _type] .type ≤ ty, acc ≠ [] ∧ (∃ i. ¬ i < 0 ∧ ¬ st[r -- _length] .intval ≤ i ∧ is_referencevalue(st[r -- i ']) ∧ acc .first = st[r -- i '] .refval ∧ junkrefs(str, acc, st[r -- _type] .type .type, st))

Rule argument

[speclemmaarg: ,st1 ⊆ st2 ↔ (∀ rk. rk ∈ st1 → rk ∈ st2 ∧ st1[rk] = st2[rk]) ,[st2, st1] → [st1, st] ,F ,store ,javastore-ostorea ,Subset ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st1, st)]]