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Proof step 8 from proof cyclic-class (previous step)

is_obj(str, r, st) ∧ st[r -- _type] .type ≤ st[r -- _type] .type, 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 = [] ∨ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ (r0 ' + refs0) .first = st[r -- fs '] .refval ∧ validrefs(str, r0 ' + refs0, fs .type, st)), ¬ r0 ∈ refs0 ∧ ¬ dups(refs0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
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), ∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ r0 = st[r -- fs '] .refval ∧ validrefs(str, st[r -- fs '] .refval ' + refs0, fs .type, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (r ' + refs) .first = r], [CSIMPSEQ : ⊦ ty ≤ ty], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' + refs ≠ []])]]