[Merged by Bors] - chore(analysis/normed_space/finite_dimension): extract some lemmas from existentials #13600
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…om existentials A few proofs in this file prove an existential where a stronger statement in terms of the witness exists. This also adds the `nnnorm` version of some `norm` lemmas.
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…om existentials (#13600) A few proofs in this file prove an existential where a stronger statement in terms of the witness exists. This: * Removes `basis.sup_norm_le_norm` and replaces it with the more general statement `pi.sum_norm_apply_le_norm` * Renames `basis.op_norm_le` to `basis.exists_op_norm_le` * Creates a new `basis.op_norm_le` stated without the existential * Adds the `nnnorm` version of some `norm` lemmas. In some cases it's easier to prove these first, and derive the `norm` versions from them.
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A few proofs in this file prove an existential where a stronger statement in terms of the witness exists.
This:
basis.sup_norm_le_normand replaces it with the more general statementpi.sum_norm_apply_le_normbasis.op_norm_letobasis.exists_op_norm_lebasis.op_norm_lestated without the existentialnnnormversion of somenormlemmas. In some cases it's easier to prove these first, and derive thenormversions from them.