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Theorems · Theorem · order theory

add_tsub_le_left

∀ {α : Type u_1} [inst : Preorder α] [inst_1 : AddCommSemigroup α] [inst_2 : Sub α] [OrderedSub α] {a b : α},
  a + b - a ≤ b

See add_tsub_cancel_left for the equality if AddLeftReflectLE α.

Defined in
Mathlib.Algebra.Order.Sub.Defs
Cited by
1 results in Mathlib
Foundations
Depth 7 from the axioms · uses propext
Assumes
PreorderAddCommSemigroupSubOrderedSub
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Around this declaration

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add_tsub_cancel_of_le · cited by 79add_tsub_cancel_of_lePreorder · cited by 7952Preorderle_rfl · cited by 1558le_rflOrderedSub · cited by 236OrderedSubAddCommSemigroup · cited by 178AddCommSemigrouptsub_le_iff_left · cited by 38tsub_le_iff_leftadd_tsub_le_leftCITED BYCITES

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Cited by1

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