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Proof step 11 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) ⊦ dups(r ' + r0 ' + refs0) ∧ (r ' + r0 ' + refs0) .first = r ∧ validrefs(str, r ' + r0 ' + refs0, st[(r ' + r0 ' + refs0) .first -- _type] .type, st), ¬ r0 ∈ refs0 ∧ ¬ dups(refs0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
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)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (r ' + refs) .first = r], [CSIMPSEQ : ⊦ ¬ r ∈ r0 ' + refs ↔ r ≠ r0 ∧ ¬ r ∈ refs], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ dups(r ' + refs) ↔ dups(refs) ∨ r ∈ refs])]]