block auto !word block capitalize abbr bcla by contradiction let's assume abbr wlg without loss of generality abbr tits that is to say, abbr wpbd we will prove the statement in both directions. abbr itf it then follows for who <- @⟨which,this⟩ for what <- @⟨means,implies⟩ abbr @⟨@who:ww,tt⟩@⟨@what:m,i⟩ @who @what abbr stam statement abbr cox counterexample abbr lcon linear combination abbr vst vector space abbr vx vertex abbr mx matrix abbr vertexs vertices abbr matrixs matrices for kind <- @⟨parts,substitution⟩ abbr ib@⟨@kind:p,s⟩ integration by @kind for kind <- @⟨independent,dependent⟩ abbr l@⟨@kind:ind,de⟩ linearly @kind for kind <- @⟨value,vector,pair⟩ abbr eg@⟨@kind:va,ve,p⟩ eigen@kind for kind <- @⟨orthogonal,orthonormal⟩ abbr @⟨@kind:ortg,ortn⟩ @kind for kind <- @⟨scalar,ordinary,linear,⟩ abbr @⟨@kind:s,o,l,⟩deq @kind differential equation