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Theorems · Theorem · order theory

div_le_comm

∀ {α : Type u} [inst : CommGroup α] [inst_1 : LE α] [MulLeftMono α] {a b c : α}, a / b ≤ c ↔ a / c ≤ b
Defined in
Mathlib.Algebra.Order.Group.Unbundled.Basic
Cited by
2 results in Mathlib
Foundations
Depth 16 from the axioms · uses propext, Quot.sound
Assumes
CommGroupLEMulLeftMono
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Around this declaration

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

Set.preimage_const_div_Iic · cited by 2Set.preimage_const_div_Iicdiv_le_of_mabs_div_le_left · cited by 1div_le_of_mabs_div_le_leftCommGroup · cited by 990CommGroupMulLeftMono · cited by 410MulLeftMonodiv_le_iff_le_mul · cited by 6div_le_iff_le_muldiv_le_iff_le_mul' · cited by 3div_le_iff_le_mul'div_le_commCITED BYCITES

Cites4

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

Cited by2

Results whose statement or proof uses this declaration.