Commit 2025-06-28 22:01 78a26d50

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chore: split WithLp.equiv into a new pair WithLp.toLp/WithLp.ofLp (#26459) (WithLp.equiv p _).symm v is very inconvenient as a normal form when working with WithLp. This introduces WithLp.toLp p v as the simp-normal spelling of this operation, and v'.ofLp as the simp-normal spelling of WithLp.equiv p _ v'. It then deprecates almost all the lemmas about WithLp.equiv, as these are no longer stated in simp-normal form. The motivation for making toLp and ofLp as plain functions, as opposed to Equivs, is to permit them to be later adapted into a constructor and projection of a one-field structure. Almost nothing in mathlib needs them to be equivs anyway. Zulip thread: [#mathlib4 > defeq abuse in `WithLp` @ 💬](https://leanprover.zulipchat.com/#narrow/channel/287929-mathlib4/topic/defeq.20abuse.20in.20.60WithLp.60/near/516241777)

Estimated changes

deleted theorem PiLp.aux_cobounded_eq
deleted theorem PiLp.aux_uniformity_eq
added theorem PiLp.continuous_ofLp
added theorem PiLp.continuous_toLp
modified def PiLp.equivₗᵢ
modified theorem PiLp.nnnorm_equiv
modified theorem PiLp.nnnorm_equiv_symm
added theorem PiLp.nnnorm_ofLp
added theorem PiLp.nnnorm_toLp
added theorem PiLp.nnnorm_toLp_const
added theorem PiLp.nnnorm_toLp_one
modified theorem PiLp.norm_equiv
modified theorem PiLp.norm_equiv_symm
added theorem PiLp.norm_ofLp
added theorem PiLp.norm_toLp
added theorem PiLp.norm_toLp_const'
added theorem PiLp.norm_toLp_const
added theorem PiLp.norm_toLp_one
added theorem PiLp.norm_toLp_single
added theorem PiLp.ofLp_apply
added theorem PiLp.toLp_apply
added theorem WithLp.dist_toLp_fst
added theorem WithLp.dist_toLp_snd
added theorem WithLp.edist_toLp_fst
added theorem WithLp.edist_toLp_snd
modified theorem WithLp.idemFst_apply
modified theorem WithLp.idemSnd_apply
added theorem WithLp.nndist_toLp_fst
added theorem WithLp.nndist_toLp_snd
added theorem WithLp.nnnorm_toLp_inl
added theorem WithLp.nnnorm_toLp_inr
added theorem WithLp.norm_toLp_fst
added theorem WithLp.norm_toLp_snd
added theorem WithLp.ofLp_fst
added theorem WithLp.ofLp_snd
modified theorem WithLp.prod_nnnorm_equiv
modified theorem WithLp.prod_norm_equiv
modified theorem WithLp.prod_norm_equiv_symm
added theorem WithLp.prod_norm_ofLp
added theorem WithLp.prod_norm_toLp
added theorem WithLp.toLp_fst
added theorem WithLp.toLp_snd
added def WithLp.ofLp
added theorem WithLp.ofLp_add
added theorem WithLp.ofLp_eq_zero
added theorem WithLp.ofLp_neg
added theorem WithLp.ofLp_smul
added theorem WithLp.ofLp_sub
added theorem WithLp.ofLp_surjective
added theorem WithLp.ofLp_toLp
added theorem WithLp.ofLp_zero
added def WithLp.toLp
added theorem WithLp.toLp_add
added theorem WithLp.toLp_eq_zero
added theorem WithLp.toLp_neg
added theorem WithLp.toLp_ofLp
added theorem WithLp.toLp_smul
added theorem WithLp.toLp_sub
added theorem WithLp.toLp_surjective
added theorem WithLp.toLp_zero