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Proof step 40 from proof validrefs-not-contains (previous step)

st[r -- i '] = refval(r0), is_array(str, r, st), st[r -- _type] .type ≤ ty, i < st[r -- _length] .intval, 0 ≤ i, 0 < st[r -- _length] .intval, is_valid_ref(str, r0, st), st[r0 -- _type] .type ≤ st[r -- _type] .type .type ⊦ r0 = jvmref, r = r0, r = jvmref, contains(str, st[r -- _type] .type, st[r0 -- _type] .type)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 32:
⊦ contains(str, ty, ty0) ↔ (∃ tys. contains(str, ty ' + (tys + ty0)))
Proof step 39:
st[r -- i '] = refval(r0), is_array(str, r, st), st[r -- _type] .type ≤ ty, i < st[r -- _length] .intval, 0 ≤ i, 0 < st[r -- _length] .intval, is_valid_ref(str, r0, st), st[r0 -- _type] .type ≤ st[r -- _type] .type .type ⊦ r0 = jvmref, r = r0, r = jvmref, ∃ tys. contains(str, st[r -- _type] .type ' + (tys + st[r0 -- _type] .type))

Rule argument

[crewrite-arg: contains-type-def , F , [ty0, ty, str] → [st[r0 -- _type] .type, st[r -- _type] .type, str] ]

Additional information

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