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Proof step 5 from proof cyclic-class (previous step)

st[r -- mkfs(class, ty, fieldvar) '] = refval(r0), validrefs(str, r0 ' + refs0, st[r0 -- _type] .type, st), is_obj(str, r, st), mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_reftype(ty), st[r0 -- _type] .type ≤ ty ⊦ validrefs(str, r0 ' + refs0, ty, st), ¬ r0 ∈ refs0 ∧ ¬ dups(refs0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ validrefs(str, refs, ty, st) ∧ ty ≤ ty0 → validrefs(str, refs, ty0, st)

Rule argument

[crewrite-arg: validrefs-superclass , F , [str, refs, ty, st, ty0] → [str, r0 ' + refs0, st[r0 -- _type] .type, st, ty] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (str, r0 ' + refs0, st[r0 -- _type] .type, st, ty)]]