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Theorems · Theorem · order theory

le_add_of_le_right

∀ {α : Type u} [inst : Add α] [inst_1 : Preorder α] [CanonicallyOrderedAdd α] {a b c : α}, a ≤ c → a ≤ b + c
Defined in
Mathlib.Algebra.Order.Monoid.Canonical.Defs
Cited by
3 results in Mathlib
Foundations
Depth 6 from the axioms · uses no axioms
Assumes
AddPreorderCanonicallyOrderedAdd
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Around this declaration

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

le_add_left · cited by 17le_add_leftSet.Finite.ecard_lt_ecard · cited by 2Finite.ecard_lt_ecardFormalMultilinearSeries.changeOrigin_eval_of_finite · cited by 1FormalMultilinearSeries.c…Preorder · cited by 7952PreorderCanonicallyOrderedAdd · cited by 229CanonicallyOrderedAddLE.le.trans' · cited by 140le.trans'le_add_self · cited by 51le_add_selfle_add_of_le_rightCITED BYCITES

Cites4

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

Cited by3

Results whose statement or proof uses this declaration.