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Proof step 10 from proof cyclic-one (previous step)

st[r -- fs '] = refval(r), st[r -- _type] .type ≤ fs .type, fs ' ∈ instfields(st[r -- _type] .type .class), is_obj(str, r, st) ⊦ validrefs(str, r ' + r ', st[r -- _type] .type, st), ∃ refs. dups(refs) ∧ refs .first = r ∧ validrefs(str, refs, st[refs .first -- _type] .type, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( validrefs(str, r ' + refs, ty, st) ↔ refs = [] ∨ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ refs .first = st[r -- fs '] .refval ∧ validrefs(str, refs, fs .type, st)))
Proof step 9:
is_obj(str, r, st) ∧ st[r -- _type] .type ≤ st[r -- _type] .type, st[r -- fs '] = refval(r), st[r -- _type] .type ≤ fs .type, fs ' ∈ instfields(st[r -- _type] .type .class), is_obj(str, r, st) ⊦ r ' = [] ∨ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ r ' .first = st[r -- fs '] .refval ∧ validrefs(str, r ', fs .type, st)), ∃ refs. dups(refs) ∧ refs .first = r ∧ validrefs(str, refs, st[refs .first -- _type] .type, st)

Rule argument

[crewrite-arg: validrefs-class , F , [st, ty, refs, r, str] → [st, st[r -- _type] .type, r ', r, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ty ≤ ty])], [EXTRATERMS : (st, st[r -- _type] .type, r ', r, str)]]