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Proof step 38 from proof validrefs-put-notin-03 (previous step)

is_obj(str, r, st), is_valid_ref(str, r, st[r -- sk, val]), st[r -- _type] .type ≤ ty, is_valid_ref(r, st) ⊦ r = jvmref, validrefs(str, r ' + r0 ' + refs1, ty, st[r -- sk, val]) ↔ validrefs(str, r ' + r0 ' + refs1, ty, st), sk = _length, sk = _type, r0 = st[r -- sk] .refval, val .refval = r0, r = r0, r0 ∈ refs1, dups(refs1), r ∈ refs1

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 37:
is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty, is_obj(str, r, st), is_valid_ref(str, r, st[r -- sk, val]), st[r -- _type] .type ≤ ty, is_valid_ref(r, st) ⊦ r = jvmref, validrefs(str, r ' + r0 ' + refs1, ty, st[r -- sk, val]) ↔ r0 ' + refs1 = [] ∨ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ (r0 ' + refs1) .first = st[r -- fs '] .refval ∧ validrefs(str, r0 ' + refs1, fs .type, st)), sk = _length, sk = _type, r0 = st[r -- sk] .refval, val .refval = r0, r = r0, r0 ∈ refs1, dups(refs1), r ∈ refs1

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, ty, r0 ' + refs1, r, str] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((1, 0, 1, 1, 1)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list, references, a, ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (st, ty, r0 ' + refs1, r, str)]]