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Proof step 25 from proof validrefs-levelsubset-01 (previous step)

is_obj(str0, r, st), level⊆(str, str0), validref(str, r, ty, st), st[r -- _type] .type ≤ ty0, is_valid_ref(str, r, st), st[r -- _type] .type ≤ ty, ∀ str, str0, ty0, st, ty. level⊆(str, str0) ∧ validrefs(str0, refs0, ty0, st) ∧ validref(str, refs0 .first, ty, st) → validrefs(str, refs0, ty0, st), refs0 = [] ∨ mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- mkfs(class, ty1, fieldvar) ']) ∧ refs0 .first = st[r -- mkfs(class, ty1, fieldvar) '] .refval ∧ validrefs(str0, refs0, ty1, st) ⊦ r = jvmref, validrefs(str, r ' + refs0, ty0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: validrefs-class antecedent: succedent: 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))) substlist: [st, ty, refs, r, str] → [st, ty0, refs0, r, str] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((1, 0, 1)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, ty0, refs0, r, str)]]