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Proof step 110 from proof exvalidrefs-nodups (previous step)

∃ refs. validrefs(str, refs, (st -- r)[r0 -- _type] .type, st -- r) ∧ refs ≠ [] ∧ ¬ dups(refs) ∧ refs .first = r0 ∧ refs .last = jvmref, st[r -- mkfs(class0, ty, fieldvar) '] = refval(r0), 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, 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, r = r0, r = jvmref, r0 = jvmref, cyclic(str, r, st), junkref(str, r0, st), ∃ 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 109:
refs .last = jvmref, st[r -- mkfs(class0, ty, fieldvar) '] = refval(refs .first), 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[refs .first -- _type] .type ≤ ty, validrefs(str, refs, st[refs .first -- _type] .type, st -- r), st[refs .first -- _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)) ⊦ r = refs .first, r = jvmref, refs .first = jvmref, refs = [], cyclic(str, r, st), junkref(str, refs .first, st), dups(refs), ∃ 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 : ⊦ ty ≤ ty0 ∧ ty0 ≤ ty1 → ty ≤ ty1], [CSIMPSEQ : ⊦ r ≠ r0 → (st -- r)[r0 -- sk0] = st[r0 -- sk0]])]]