Theorems · Definition · order theory
EReal.rec
{motive : EReal → Sort u_1} → motive ⊥ → ((a : ℝ) → motive ↑a) → motive ⊤ → (a : EReal) → motive aA recursor for EReal in terms of the coercion.
When working in term mode, note that pattern matching can be used directly,
although this is prone to leaking the implementation details in terms of Option.
- Defined in
- Mathlib.Data.EReal.Basic
- Cited by
- 57 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Top.topstatement and proof · cited by 9,680
- Bot.botstatement and proof · cited by 4,720
- ERealstatement and proof · cited by 793
- Real.toERealstatement and proof · cited by 303
Cited by58
Results whose statement or proof uses this declaration.
- EReal.expproof · cited by 46
- EReal.mul_commproof · cited by 16
- EReal.top_add_of_ne_botproof · cited by 10
- EReal.log_expproof · cited by 6
- EReal.inv_nonneg_of_nonnegproof · cited by 6
- EReal.top_subproof · cited by 6
- EReal.sub_botproof · cited by 5
- EReal.neg_addproof · cited by 4
- EReal.sub_le_of_le_addproof · cited by 3
- EReal.exists_between_coe_realproof · cited by 3
- EReal.exp_strictMonoproof · cited by 3
- EReal.continuousAt_addproof · cited by 2