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Proof step 143 from proof exvalidrefs-nodups (previous step)

ty = mkclasstype(class2), st[r -- _type] .type = mkclasstype(class1), class1 ≤ class, class+∃(str, class1), is_obj(r, st), mkfs(class0, ty, fieldvar) ' ∈ instfields(class), ty ≤ mkclasstype(class), is_classtype(ty), class1 ≤ class2, ∀ 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)) ⊦ r = jvmref, is_referencevalue(st[r -- mkfs(class0, ty, fieldvar) ']), cyclic(str, r, st), is_abstract(class1), ∃ refs. validrefs(str, refs, st[refs .first -- _type] .type, st) ∧ refs ≠ [] ∧ ¬ dups(refs) ∧ refs .first = r ∧ refs .last = jvmref

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 142:
st[r -- _type] .type = mkclasstype(class1), class1 ≤ class2, class+∃(str, class1), is_obj(r, st), mkfs(class0, mkclasstype(class2), fieldvar) ' ∈ instfields(class), class2 ≤ class, class1 ≤ 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)) ⊦ r = jvmref, is_referencevalue(st[r -- mkfs(class0, mkclasstype(class2), fieldvar) ']), cyclic(str, r, st), is_abstract(class1), ∃ refs. validrefs(str, refs, st[refs .first -- _type] .type, st) ∧ refs ≠ [] ∧ ¬ dups(refs) ∧ refs .first = r ∧ refs .last = jvmref

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ class1 ≤ class2 ∧ class2 ≤ class3 → class1 ≤ class3], [CSIMPSEQ : ⊦ is_classtype(mkclasstype(class))], [CSIMPSEQ : ⊦ mkclasstype(class1) ≤ mkclasstype(class2) ↔ class1 ≤ class2])]]