`oneDimSubspace_closed`

proved

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module: IndisputableMonolith.Algebra.F2Power
domain: Algebra
line: 250 · github
papers citing: none yet

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IndisputableMonolith.Algebra.F2Power on GitHub at line 250.

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formal source

 247  simp [Finset.card_insert_of_notMem, Ne.symm hv]
 248
 249/-- The 1-dimensional subspace is closed under addition. -/
 250theorem oneDimSubspace_closed (v : F2Power D) (a b : F2Power D)
 251    (ha : a ∈ oneDimSubspace v) (hb : b ∈ oneDimSubspace v) :
 252    a + b ∈ oneDimSubspace v := by
 253  unfold oneDimSubspace at ha hb ⊢
 254  simp [Finset.mem_insert, Finset.mem_singleton] at ha hb ⊢
 255  rcases ha with ha | ha <;> rcases hb with hb | hb <;>
 256    subst_vars <;> simp [add_self]
 257
 258end F2Power
 259
 260end Algebra
 261end IndisputableMonolith

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