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Theorems · Theorem · order theory

sub_lt_sub_iff_left

∀ {α : Type u} [inst : AddGroup α] [inst_1 : LT α] [AddLeftStrictMono α] [AddRightStrictMono α] {b c : α} (a : α),
  a - b < a - c ↔ c < b
Defined in
Mathlib.Algebra.Order.Group.Unbundled.Basic
Cited by
3 results in Mathlib
Foundations
Depth 15 from the axioms · uses propext
Assumes
AddGroupLTAddLeftStrictMonoAddRightStrictMono
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

sub_lt_sub_left · cited by 9sub_lt_sub_leftnhds_eq_iInf_abs_sub · cited by 5nhds_eq_iInf_abs_subReal.exists_rat_eq_convergent' · cited by 1Real.exists_rat_eq_conver…AddGroup · cited by 4410AddGroupsub_eq_add_neg · cited by 1023sub_eq_add_negAddLeftStrictMono · cited by 203AddLeftStrictMonoAddRightStrictMono · cited by 160AddRightStrictMononeg_add_cancel_left · cited by 84neg_add_cancel_leftneg_lt_neg_iff · cited by 39neg_lt_neg_iffadd_lt_add_iff_left · cited by 30add_lt_add_iff_leftsub_lt_sub_iff_leftCITED BYCITES

Cites7

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Cited by3

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