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Proof step 6 from proof unchanged-pathex (previous step)

unchanged(str, r, st, st1), validrefs(str, r ' + refs0, mkclasstype(`java.lang.Object' .class), st), r0 ∈ refs0 ⊦ r0 = r, validrefs(str, r ' + refs0, mkclasstype(`java.lang.Object' .class), st1), unchangedNorec(r0, st, st1), path∃(str, r, r0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ validrefs(str, r ' + refs, ty, st) ∧ r0 ∈ refs → path∃(str, r, r0, st)

Rule argument

[x0lemmaarg: spec-name: cyclic instance-name: lemma-name: pathex-validrefs-in antecedent: succedent: validrefs(str, r ' + refs, ty, st) ∧ r0 ∈ refs → path∃(str, r, r0, st) substlist: [str, r, refs, ty, st, r0] → [str, r, refs0, mkclasstype(`java.lang.Object' .class), st, r0] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 3)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (str, r, refs0, mkclasstype(`java.lang.Object' .class), st, r0)]]