lt_add_one — Mathlib

English

The zero-augmented endomorphism is strictly increasing under the LocallyFiniteOrder assumptions.

Русский

Зеро-усиленный эндоморфизм возрастает строго при условиях LocallyFiniteOrder.

LaTeX

$$orderMonoidWithZeroHom_strictMono$$

Lean4

theorem lt_add_one [One α] [AddZeroClass α] [PartialOrder α] [ZeroLEOneClass α] [NeZero (1 : α)] [AddLeftStrictMono α]
    (a : α) : a < a + 1 :=
  lt_add_of_pos_right _ zero_lt_one

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