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Proof step 19 from proof cyclic-def-object (previous step)

is_obj(str, r, st), refs1 = [] ∨ mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- mkfs(class, ty, fieldvar) ']) ∧ refs1 .first = st[r -- mkfs(class, ty, fieldvar) '] .refval ∧ validrefs(str, refs1, ty, st) ⊦ r = jvmref, validrefs(str, r ' + refs1, mkclasstype(`java.lang.Object' .class), st), ¬ r ∈ refs1 ∧ ¬ dups(refs1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ 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 12:
¬ (is_obj(str, r, st) ∧ st[r -- _type] .type ≤ mkclasstype(`java.lang.Object' .class)), is_obj(str, r, st), refs1 = [] ∨ mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- mkfs(class, ty, fieldvar) ']) ∧ refs1 .first = st[r -- mkfs(class, ty, fieldvar) '] .refval ∧ validrefs(str, refs1, ty, st) ⊦ r = jvmref, validrefs(str, r ' + refs1, mkclasstype(`java.lang.Object' .class), st), ¬ r ∈ refs1 ∧ ¬ dups(refs1)
Proof step 18:
is_obj(str, r, st) ∧ st[r -- _type] .type ≤ mkclasstype(`java.lang.Object' .class), is_obj(str, r, st), refs1 = [] ∨ mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- mkfs(class, ty, fieldvar) ']) ∧ refs1 .first = st[r -- mkfs(class, ty, fieldvar) '] .refval ∧ validrefs(str, refs1, ty, st) ⊦ r = jvmref, refs1 = [] ∨ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ refs1 .first = st[r -- fs '] .refval ∧ validrefs(str, refs1, fs .type, st)), ¬ r ∈ refs1 ∧ ¬ dups(refs1)

Rule argument

[crewrite-arg: validrefs-class , F , [st, ty, refs, r, str] → [st, mkclasstype(`java.lang.Object' .class), refs1, r, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, mkclasstype(`java.lang.Object' .class), refs1, r, str)]]