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Proof step 101 from proof exvalidrefs-nodups (previous step)

st[r -- mkfs(class0, ty, fieldvar) '] = refval(r0), refs0 .last = jvmref, st[r -- _type] .type ≤ mkclasstype(class), st[r -- _type] .type ≤ ty, ty ≤ mkclasstype(class), mkfs(class0, ty, fieldvar) ' ∈ instfields(class), is_obj(str, r, st), is_classtype(st[r -- _type] .type), st[r0 -- _type] .type ≤ ty, validrefs(str, r0 ' + refs0, st[r0 -- _type] .type, st -- r), 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)) ⊦ refs0 = [], r = r0, r = jvmref, r0 = jvmref, cyclic(str, r, st), junkref(str, r0, st), dups(refs0), r0 ∈ refs0, ∃ refs. validrefs(str, refs, st[refs .first -- _type] .type, st) ∧ refs ≠ [] ∧ ¬ dups(refs) ∧ refs .first = r ∧ refs .last = jvmref, (∃ 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)) ∧ ¬ r ∈ refs0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 100:
st[r -- _type] .type = mkclasstype(class1), st[r -- mkfs(class0, ty, fieldvar) '] = refval(r0), refs0 .last = jvmref, st[r -- _type] .type ≤ mkclasstype(class), st[r -- _type] .type ≤ ty, ty ≤ mkclasstype(class), mkfs(class0, ty, fieldvar) ' ∈ instfields(class), is_obj(str, r, st), is_classtype(st[r -- _type] .type), st[r0 -- _type] .type ≤ ty, validrefs(str, r0 ' + refs0, st[r0 -- _type] .type, st -- r), 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)) ⊦ refs0 = [], r = r0, r = jvmref, r0 = jvmref, cyclic(str, r, st), junkref(str, r0, st), dups(refs0), r0 ∈ refs0, ∃ refs. validrefs(str, refs, st[refs .first -- _type] .type, st) ∧ refs ≠ [] ∧ ¬ dups(refs) ∧ refs .first = r ∧ refs .last = jvmref, (∃ fs. fs ' ∈ instfields(class1) ∧ is_referencevalue(st[r -- fs ']) ∧ r0 = st[r -- fs '] .refval ∧ validrefs(str, st[r -- fs '] .refval ' + refs0, fs .type, st)) ∧ ¬ r ∈ refs0

Rule argument

[speclemmaarg: ,is_classtype(ty) → (class = ty .class ↔ ty = mkclasstype(class)) ,[ty, class] → [st[r -- _type] .type, class1] ,T ,javatype , ,elim-02 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_classtype(ty) → ( class = ty .class ↔ ty = mkclasstype(class))])], [EXTRATERMS : (st[r -- _type] .type, class1)]]