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Proof step 97 from proof exvalidrefs-maxlength (previous step)

refs0 = refs1 + r1 ', st[r -- mkfs(class, ty, fieldvar) '] = refval(r0), validrefs(str, r0 ' + refs0, st[r0 -- _type] .type, st -- r), st[r0 -- _type] .type ≤ ty, is_reftype(ty), mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_obj(str, r, st), is_obj(r, st), ∀ r, str, st0. # st0 .refs < # st .refs → ( true → cyclic(str, r, st0) ∨ junkref(str, r, st0) ∨ (∃ refs. validrefs(str, refs, st0[refs .first -- _type] .type, st0) ∧ refs ≠ [] ∧ ¬ dups(refs) ∧ refs .first = r ∧ ¬ has_reffield(refs .last, st0))) ⊦ refs0 = [], r0 = jvmref, r = jvmref, r = r0, r0 ∈ refs0, dups(refs0), has_reffield(r1, st -- r), junkref(str, r0, st), cyclic(str, r, st), ∃ refs. validrefs(str, refs, st[refs .first -- _type] .type, st) ∧ refs ≠ [] ∧ ¬ dups(refs) ∧ refs .first = r ∧ ¬ has_reffield(refs .last, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 96:
st[r -- mkfs(class, ty, fieldvar) '] = refval(r0), validrefs(str, r0 ' + refs1 + r1 ', st[r0 -- _type] .type, st -- r), st[r0 -- _type] .type ≤ ty, is_reftype(ty), mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_obj(str, r, st), is_obj(r, st), ∀ r, str, st0. # st0 .refs < # st .refs → ( true → cyclic(str, r, st0) ∨ junkref(str, r, st0) ∨ (∃ refs. validrefs(str, refs, st0[refs .first -- _type] .type, st0) ∧ refs ≠ [] ∧ ¬ dups(refs) ∧ refs .first = r ∧ ¬ has_reffield(refs .last, st0))) ⊦ r0 = jvmref, r = jvmref, r = r0, r0 = r1, has_reffield(r1, st -- r), junkref(str, r0, st), cyclic(str, r, st), r0 ∈ refs1, r1 ∈ refs1, dups(refs1), ∃ refs. validrefs(str, refs, st[refs .first -- _type] .type, st) ∧ refs ≠ [] ∧ ¬ dups(refs) ∧ refs .first = r ∧ ¬ has_reffield(refs .last, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ dups(refs + r ') ↔ r ∈ refs ∨ dups(refs)], [CSIMPSEQ : ⊦ r ∈ r0 ' ↔ r = r0], [CSIMPSEQ : ⊦ r ∈ refs + refs0 ↔ ¬ ¬ (r ∈ refs ∨ r ∈ refs0)], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ refs + r ' ≠ []])]]