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[Merged by Bors] - chore(Data/Finsupp/Fin): add Finsupp.cons_support #10192

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[Merged by Bors] - chore(Data/Finsupp/Fin): add Finsupp.cons_support #10192

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7 changes: 7 additions & 0 deletions Mathlib/Data/Finsupp/Fin.lean
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Expand Up @@ -92,4 +92,11 @@ theorem cons_ne_zero_iff : cons y s ≠ 0 ↔ y ≠ 0 ∨ s ≠ 0 := by
rw [h', c, Finsupp.cons_zero_zero]
#align finsupp.cons_ne_zero_iff Finsupp.cons_ne_zero_iff

lemma cons_support : (s.cons y).support ⊆ insert 0 (s.support.map (Fin.succEmb n).toEmbedding) := by
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Do we have a similar lemma about Fin.cons? IMHO, lemmas about Finsupp.cons should be mod_cast (lemma about Fin.cons), if possible.

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What would the lemma about Fin.cons be? The ingredients in the statement seem quite Finsupp-specific.

intro i hi
suffices i = 0 ∨ ∃ a, ¬s a = 0 ∧ a.succ = i by simpa
apply (Fin.eq_zero_or_eq_succ i).imp id (Exists.imp _)
rintro i rfl
simpa [Finsupp.mem_support_iff] using hi

end Finsupp
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