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Proof step 91 from proof exvalidrefs-maxlength (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 90:
st[r -- mkfs(class, ty, fieldvar) '] = refval(r0), is_obj(r, st), is_obj(str, r, st), mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_reftype(ty), st[r0 -- _type] .type ≤ ty, validrefs(str, r0 ' + refs1 + r1 ', st[r0 -- _type] .type, st -- r), validrefs(str, r0 ' + refs1 + r1 ', st[r0 -- _type] .type, 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))) ⊦ r = r1, r0 = r1, r = r0, r = jvmref, r0 = jvmref, has_reffield(r1, st), r ∈ refs1, dups(refs1), r1 ∈ refs1, r0 ∈ refs1, cyclic(str, r, st), junkref(str, r0, st), validrefs(str, r ' + r0 ' + refs1 + r1 ', st[r -- _type] .type, st)

Rule argument

[emptyarg]

Additional information

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