Theorems · Theorem · real analysis
OrderedFinpartition.one_lt_partSize_index_zero
∀ {n : ℕ} (c : OrderedFinpartition (n + 1)), Set.range (c.emb 0) ≠ {0} → 1 < c.partSize (c.index 0)If the left-most part is not {0}, then the part containing 0 has at least two elements:
either because it's the left-most part, and then it's not just 0 by assumption, or because it's
not the left-most part and then, by increasingness of maximal elements in parts, it contains
a positive element.
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- 0 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
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