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Proof step 11 from proof exvalidrefs-nodups (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( validrefs(str, r ' + refs, ty, st) ↔ refs = [] ∨ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ refs .first = st[r -- fs '] .refval ∧ validrefs(str, refs, fs .type, st)))
Proof step 10:
is_obj(str, r0, st) ∧ st[r0 -- _type] .type ≤ st[r0 -- _type] .type, st[r0 -- mkfs(class0, ty, fieldvar) '] = refval(r0), ty ≤ mkclasstype(class), mkfs(class0, ty, fieldvar) ' ∈ instfields(class), is_obj(str, r0, st), is_classtype(st[r0 -- _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, junkref(str, r0, st), r0 ' = [] ∨ (∃ fs. fs ' ∈ instfields(st[r0 -- _type] .type .class) ∧ is_referencevalue(st[r0 -- fs ']) ∧ r0 ' .first = st[r0 -- fs '] .refval ∧ validrefs(str, r0 ', fs .type, st)), ∃ refs. validrefs(str, refs, st[refs .first -- _type] .type, st) ∧ refs ≠ [] ∧ ¬ dups(refs) ∧ refs .first = r0 ∧ refs .last = jvmref

Rule argument

[crewrite-arg: validrefs-class , F , [st, ty, refs, r, str] → [st, st[r0 -- _type] .type, r0 ', r0, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ty ≤ ty])], [EXTRATERMS : (st, st[r0 -- _type] .type, r0 ', r0, str)]]