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Commit 2022-04-09 19:44 cc65716e

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refactor(analysis/complex): replace diff_on_int_cont with diff_cont_on_cl (#13148) Use "differentiable on a set and continuous on its closure" instead of "continuous on a set and differentiable on its interior". There are a few reasons to prefer the latter:

  • it has better "composition" lemma;
  • it allows us to talk about functions that are, e.g., differentiable on {z : ℂ | abs z < 1 ∧ (re z < 0 ∨ im z ≠ 0)} and continuous on the closed unit disk. Also generalize eq_on_of_eq_on_frontier from a compact set to a bounded set (so that it works, e.g., for the unit ball in a Banach space). This PR does not move the file diff_on_int_cont to make the diff more readable; the file will be moved in another PR.

Estimated changes

added theorem diff_cont_on_cl.add
added theorem diff_cont_on_cl.comp
added theorem diff_cont_on_cl.inv
added theorem diff_cont_on_cl.neg
added theorem diff_cont_on_cl.smul
added theorem diff_cont_on_cl.sub
added structure diff_cont_on_cl
added theorem diff_cont_on_cl_const
added theorem diff_cont_on_cl_univ
deleted theorem diff_on_int_cont.add
deleted theorem diff_on_int_cont.comp
deleted theorem diff_on_int_cont.inv
deleted theorem diff_on_int_cont.mk_ball
deleted theorem diff_on_int_cont.neg
deleted theorem diff_on_int_cont.smul
deleted theorem diff_on_int_cont.sub
deleted structure diff_on_int_cont
deleted theorem diff_on_int_cont_const
deleted theorem diff_on_int_cont_open
deleted theorem diff_on_int_cont_univ