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Proof step 37 from proof exvalidrefs-nodups (previous step)

st[r -- mkfs(class0, ty, fieldvar) '] = refval(r0), is_obj(str, r0, st), 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), junkrefs(str, (r0 ' + refs) + r ', st[r0 -- _type] .type, st -- r), ∀ 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 = r0, r = jvmref, r0 = jvmref, r ∈ refs, junkref(str, r0, st), dups(r ' + (r0 ' + refs) + r ') ∧ (r ' + (r0 ' + refs) + r ') .first = r ∧ validrefs(str, r ' + (r0 ' + refs) + r ', st[(r ' + (r0 ' + refs) + r ') .first -- _type] .type, 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 36:
st[r -- mkfs(class0, ty, fieldvar) '] = refval(r0), is_obj(str, r0, st), 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), junkrefs(str, (r0 ' + refs) + r ', st[r0 -- _type] .type, st -- r), ∀ 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 = r0, r = jvmref, r0 = jvmref, r ∈ refs, junkref(str, r0, st), validrefs(str, r ' + (r0 ' + refs) + r ', st[r -- _type] .type, st), ∃ 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 : ([CSIMPSEQ : ⊦ (r ' + refs) .first = r], [CSIMPSEQ : ⊦ r ≠ r0 → (r ∈ r0 ' + refs ↔ r ∈ refs)], [CSIMPSEQ : ⊦ r ∈ r0 ' ↔ r = r0], [CSIMPSEQ : ⊦ r ∈ refs + refs0 ↔ ¬ ¬ (r ∈ refs ∨ r ∈ refs0)], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ dups(refs + r ') ↔ r ∈ refs ∨ dups(refs)], [CSIMPSEQ : ⊦ dups(r ' + refs) ↔ dups(refs) ∨ r ∈ refs])]]