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Commit 2022-07-17 15:25 fcceffa0

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chore(order/initial_seg): move definitions of initial and principal segments (#15328) We move the definitions of initial and principal segments from set_theory/ordinal/basic.lean to a new file order/initial_seg.lean. We minimally change this file, just doing the following:

  • add a copyright header
  • copy over existing documentation
  • add a few noncomputable attributes
  • localize the notation
  • use by_cases in initial_seg.lt_or_eq (needed as the classical locale is no longer open)

Estimated changes

added theorem initial_seg.coe_coe_fn
added theorem initial_seg.coe_fn_mk
added theorem initial_seg.init'
added theorem initial_seg.init_iff
added theorem initial_seg.refl_apply
added structure initial_seg
added theorem principal_seg.down'
added theorem principal_seg.init
added theorem principal_seg.init_iff
added theorem principal_seg.irrefl
added theorem principal_seg.lt_top
added theorem principal_seg.top_eq
added structure principal_seg
deleted theorem initial_seg.antisymm.aux
deleted theorem initial_seg.antisymm_symm
deleted theorem initial_seg.coe_coe_fn
deleted theorem initial_seg.coe_fn_mk
deleted theorem initial_seg.init'
deleted theorem initial_seg.init_iff
deleted def initial_seg.le_add
deleted theorem initial_seg.le_add_apply
deleted def initial_seg.le_lt
deleted theorem initial_seg.le_lt_apply
deleted def initial_seg.of_iso
deleted theorem initial_seg.refl_apply
deleted theorem initial_seg.trans_apply
deleted structure initial_seg
deleted theorem principal_seg.coe_coe_fn'
deleted theorem principal_seg.coe_coe_fn
deleted theorem principal_seg.coe_fn_mk
deleted theorem principal_seg.down'
deleted theorem principal_seg.init
deleted theorem principal_seg.init_iff
deleted theorem principal_seg.irrefl
deleted def principal_seg.lt_le
deleted theorem principal_seg.lt_le_apply
deleted theorem principal_seg.lt_le_top
deleted theorem principal_seg.lt_top
deleted theorem principal_seg.top_eq
deleted theorem principal_seg.top_lt_top
deleted theorem principal_seg.trans_apply
deleted theorem principal_seg.trans_top
deleted structure principal_seg