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Theorems · Theorem · order theory

add_left_mono

∀ {α : Type u_1} [inst : Add α] [inst_1 : Preorder α] [AddRightMono α] {a : α}, Monotone fun x => x + a
Defined in
Mathlib.Algebra.Order.Monoid.Unbundled.Basic
Cited by
9 results in Mathlib
Foundations
Depth 6 from the axioms · uses no axioms
Assumes
AddPreorderAddRightMono
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Around this declaration

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

Monotone.add_const · cited by 7Monotone.add_constadd_left_strictMono_of_ne_top · cited by 3add_left_strictMono_of_ne…Filter.map_add_atTop_eq · cited by 1Filter.map_add_atTop_eqseminormFromConst_const_mul · cited by 1seminormFromConst_const_m…min_add · cited by 0min_addAntitone.add_const · cited by 0Antitone.add_constAntitoneOn.add_const · cited by 0AntitoneOn.add_constmax_add · cited by 0max_addMonotoneOn.add_const · cited by 0MonotoneOn.add_constPreorder · cited by 7952PreorderMonotone · cited by 1397MonotoneAddRightMono · cited by 367AddRightMonoadd_le_add_left · cited by 37add_le_add_leftadd_left_monoCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by9

Results whose statement or proof uses this declaration.