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Proof step 17 from proof validrefs-levelsubset-01 (previous step)

st[r -- mkfs(class, ty1, fieldvar) '] = refval(r0), is_obj(str, r, st), is_obj(str0, r, st), level⊆(str, str0), validref(str, r, ty, st), st[r -- _type] .type ≤ ty0, st[r -- _type] .type ≤ ty, mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), validrefs(str0, r0 ' + refs, ty1, st), ∀ str1, str2, ty2, st0, ty3. level⊆(str1, str2) ∧ validrefs(str2, r0 ' + refs, ty2, st0) ∧ validref(str1, r0, ty3, st0) → validrefs(str1, r0 ' + refs, ty2, st0) ⊦ r = jvmref, validrefs(str, r0 ' + refs, ty1, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[x0lemmaarg: spec-name: junkrefs instance-name: lemma-name: validref-class-rec antecedent: succedent: is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( validref(str, r, ty, st) ↔ ¬ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ st[r -- fs '] .refval ≠ jvmref ∧ ( ¬ st[st[r -- fs '] .refval -- _type] .type ≤ fs .type ∨ ¬ validref (str, st[r -- fs '] .refval, fs .type, st)))) substlist: [st, ty, r, str] → [st, ty, r, str] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 4)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, ty, r, str)]]