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

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

User applied rule case distinction

And obtained the following new goals

Proof step 9:
st[r -- mkfs(class, ty, fieldvar) '] = refval(r0), st[r0 -- _type] .type ≤ ty, is_reftype(ty), mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_obj(str, r, st), validrefs(str, r0 ' + refs0, st[r0 -- _type] .type, st) ⊦ validrefs(str, r ' + r0 ' + refs0, st[r -- _type] .type, st), ¬ r0 ∈ refs0 ∧ ¬ dups(refs0)

Rule argument

[CASEDARG : pos: right 2, ()]

Additional information

[[CONCRETESIMPRULES : ()]]