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Theorems · Theorem · combinatorics

Finite.not_infinite

∀ {α : Sort u_1}, Finite α → ¬Infinite α

Alias of the reverse direction of not_infinite_iff_finite.

Defined in
Mathlib.Data.Finite.Defs
Cited by
2 results in Mathlib
Foundations
Depth 15 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

PiTensorProduct.ext_of_span_eq_top · cited by 2PiTensorProduct.ext_of_sp…Module.not_finite_of_infinite_basis · cited by 1Module.not_finite_of_infi…Finite · cited by 3029FiniteInfinite · cited by 352Infinitenot_infinite_iff_finite · cited by 3not_infinite_iff_finiteFinite.not_infiniteCITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.