Theorems · Theorem · order theory

forall_lt_add_iff_lt_right

∀ {α : Type u_1} [inst : LinearOrder α] {P : α → Prop} {b c : α} [inst_1 : AddCommMagma α] [CanonicallyOrderedAdd α]
  [AddLeftReflectLT α] [IsLeftCancelAdd α], (∀ a < b + c, P a) ↔ (∀ a < c, P a) ∧ ∀ d < b, P (d + c)

Defined in: Mathlib.Algebra.Order.Monoid.Canonical.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: LinearOrder AddCommMagma CanonicallyOrderedAdd AddLeftReflectLT IsLeftCancelAdd

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LinearOrderstatement and proof · cited by 8,572
CanonicallyOrderedAddstatement and proof · cited by 229
IsLeftCancelAddstatement and proof · cited by 72
AddLeftReflectLTstatement and proof · cited by 33
AddCommMagmastatement and proof · cited by 32

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