Theorems · Theorem · complex analysis
Real.add_one_lt_exp
∀ {x : ℝ}, x ≠ 0 → x + 1 < Real.exp x- Defined in
- Mathlib.Analysis.Complex.Exponential
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Nat.cast_oneproof · cited by 2,501
- Nat.cast_zeroproof · cited by 1,870
- add_commproof · cited by 1,535
- Real.expstatement and proof · cited by 871
- one_divproof · cited by 624
- lt_of_not_geproof · cited by 374
- le_or_gtproof · cited by 269
- sub_neg_eq_addproof · cited by 264
- Real.exp_posproof · cited by 169
- Ne.lt_or_gtproof · cited by 108
- neg_posproof · cited by 74
Cited by4
Results whose statement or proof uses this declaration.
- Real.add_one_le_expproof · cited by 13
- Real.log_lt_sub_one_of_posproof · cited by 4
- strictConvexOn_expproof · cited by 2
- Real.one_sub_lt_exp_negproof · cited by 0