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Proof step 17 from proof sources-rec-01 (previous step)

⊦ cl = [], sources(cl, d) = (((∃ d0. d0 ∈ sources(cl .rest, d) ∧ cdom(cl .first) ⇒ d0) ⊃ sources(cl .rest, d) ++ cdom(cl .first); sources(cl .rest, d)))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 16:
cl = co + cl0 ⊦ cl = [], sources(cl, d) = (((∃ d0. d0 ∈ sources(cl0, d) ∧ cdom(co) ⇒ d0) ⊃ sources(cl0, d) ++ cdom(co); sources(cl0, d)))

Rule argument

[x0lemmaarg: spec-name: list-data instance-name: gen-command-list lemma-name: elim-list-c antecedent: cl ≠ [] succedent: co = cl .first ∧ cl0 = cl .rest ↔ cl = co + cl0 substlist: [cl, co, cl0] → [cl, co, cl0] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : cl ≠ [] ⊦ co = cl .first ∧ cl0 = cl .rest ↔ cl = co + cl0])], [EXTRATERMS : (cl, co, cl0)]]