measurableSet_sigma_fst_lt
From the authors
The set of elements of Σ n : ℕ, X n with first component less than M is measurable.
-
X : ℕ → Type u_4(n : ℕ) → MeasurableSpace (X n)A measurable space is a space equipped with a σ-algebra. -
M : ℕ
MeasurableSet {x | x.fst < M}MeasurableSet s means that s is measurable (in the ambient measure space on α)MeasurableSpace : Type u_6 → Type u_6A measurable space is a space equipped with a σ-algebra.
Nat : TypeThe natural numbers, starting at zero. This type is special-cased by both the kernel and the compiler, and overridden with an efficient implementation. Both use a fast arbitrary-precision arithmetic library (usually [GMP](https://gmplib.org/)); at runtime, `Nat` values that are sufficiently small are unboxed.
MeasurableSet : {α : Type u_1} → [MeasurableSpace α] → Set α → Prop`MeasurableSet s` means that `s` is measurable (in the ambient measure space on `α`)
Set.ofPred : {α : Type u} → (α → Prop) → Set αTurn a predicate `p : α → Prop` into a set, also written as `{x | p x}`Sigma.fst : {α : Type u} → {β : α → Type v} → Sigma β → αThe first component of a dependent pair.
LT.lt : {α : Type u} → [self : LT α] → α → α → PropThe less-than relation: `x < y` Conventions for notations in identifiers: * The recommended spelling of `<` in identifiers is `lt`.
Code
lemma measurableSet_sigma_fst_lt (M : ℕ) : MeasurableSet {x : Σ n, X n | x.1 < M}Proof
measurable_sigma_fst (MeasurableSet.of_discrete (s := Set.Iio M))
New in v4.34.0-rc2-82-ga6c27a7 (2026-09-13), and its meaning has not changed since.
Self-contained, with its dependencies inlined and proofs replaced by sorry: download the raw file · open it in the Lean web editor.
Dependency graph
Nothing to draw. Its statement rests on no other declaration in this project, and names nothing from a package left unaudited — so the graph is this declaration alone. That is the answer, not a missing picture.
Audit surface: 0 project declarations, 9 external constants
✓ Proved: no sorry anywhere in its closure
This is the tool's own reading of one build's recorded axioms, and it is not robust against an author who wants it to pass. Checking meant to be relied on should go through Comparator, which replays the proof through the kernel from an export against an explicit list of permitted axioms.