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Proof step 21 from proof validrefs-not-contains (previous step)

st[r -- mkfs(class, ty0, fieldvar) '] = refval(r0), is_obj(str, r, st), st[r -- _type] .type ≤ ty, mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_valid_ref(str, r0, st), st[r0 -- _type] .type ≤ ty0 ⊦ 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 5:
⊦ contains(str, ty, ty0) ↔ (∃ tys. contains(str, ty ' + (tys + ty0)))
Proof step 20:
st[r -- mkfs(class, ty0, fieldvar) '] = refval(r0), is_obj(str, r, st), st[r -- _type] .type ≤ ty, mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_valid_ref(str, r0, st), st[r0 -- _type] .type ≤ ty0 ⊦ 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)]]