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Mathlib.LinearAlgebra.Dimension.Subsingleton

Dimension of trivial modules #

@[simp]
theorem rank_subsingleton' (R : Type u_1) (M : Type u_2) [Semiring R] [AddCommMonoid M] [Module R M] [Nontrivial R] [Subsingleton M] :
Module.rank R M = 0

See rank_subsingleton that assumes Subsingleton R instead.

theorem rank_punit (R : Type u_1) [Semiring R] [Nontrivial R] :
Module.rank R PUnit.{u_3 + 1} = 0
theorem rank_bot (R : Type u_1) (M : Type u_2) [Semiring R] [AddCommMonoid M] [Module R M] [Nontrivial R] :
Module.rank R = 0