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Proof step 8 from proof exvalidrefs-nodups (previous step)

st[r0 -- mkfs(class0, ty, fieldvar) '] = refval(r0), ty ≤ mkclasstype(class), mkfs(class0, ty, fieldvar) ' ∈ instfields(class), is_obj(str, r0, st), is_classtype(st[r0 -- _type] .type), st[r0 -- _type] .type ≤ ty, st[r0 -- _type] .type ≤ mkclasstype(class), ∀ r, str, st0. # st0 .refs < # st .refs → ( ¬ junkref(str, r, st0) ∧ ¬ cyclic(str, r, st0) ∧ is_obj(str, r, st0) ∧ r ≠ jvmref ∧ (∃ fs, class. fs ' ∈ instfields(class) ∧ fs .type ≤ mkclasstype(class) ∧ st0[r -- _type] .type ≤ fs .type) → (∃ refs. validrefs(str, refs, st0[r -- _type] .type, st0) ∧ refs ≠ [] ∧ ¬ dups(refs) ∧ refs .first = r ∧ refs .last = jvmref)) ⊦ r0 = jvmref, junkref(str, r0, st), ∃ refs. validrefs(str, refs, st[refs .first -- _type] .type, st) ∧ refs ≠ [] ∧ ¬ dups(refs) ∧ refs .first = r0 ∧ refs .last = jvmref, mkfs(class0, ty, fieldvar) ' ∈ instfields(st[r0 -- _type] .type .class) ∧ is_referencevalue(st[r0 -- mkfs(class0, ty, fieldvar) ']) ∧ r0 = st[r0 -- mkfs(class0, ty, fieldvar) '] .refval ∧ validrefs(str, r0 ', mkfs(class0, ty, fieldvar) .type, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
st[r0 -- mkfs(class0, ty, fieldvar) '] = refval(r0), st[r0 -- _type] .type ≤ mkclasstype(class), st[r0 -- _type] .type ≤ ty, is_classtype(st[r0 -- _type] .type), is_obj(str, r0, st), mkfs(class0, ty, fieldvar) ' ∈ instfields(class), ty ≤ mkclasstype(class), ∀ r, str, st0. # st0 .refs < # st .refs → ( ¬ junkref(str, r, st0) ∧ ¬ cyclic(str, r, st0) ∧ is_obj(str, r, st0) ∧ r ≠ jvmref ∧ (∃ fs, class. fs ' ∈ instfields(class) ∧ fs .type ≤ mkclasstype(class) ∧ st0[r -- _type] .type ≤ fs .type) → (∃ refs. validrefs(str, refs, st0[r -- _type] .type, st0) ∧ refs ≠ [] ∧ ¬ dups(refs) ∧ refs .first = r ∧ refs .last = jvmref)) ⊦ r0 = jvmref, junkref(str, r0, st), validrefs(str, r0 ', ty, st), ∃ refs. validrefs(str, refs, st[refs .first -- _type] .type, st) ∧ refs ≠ [] ∧ ¬ dups(refs) ∧ refs .first = r0 ∧ refs .last = jvmref

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))], [CSIMPSEQ : ⊦ mkfs(class, ty, fieldvar) .type = ty], [CSIMPSEQ : ⊦ fs ' ∈ instfields(class) ∧ ty ≤ mkclasstype(class) ∧ is_classtype(ty) → fs ' ∈ instfields(ty .class)])]]