fix: scope Exercise 1.2.2's boundedness hypothesis to its own conjunct - #650
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fix: scope Exercise 1.2.2's boundedness hypothesis to its own conjunct#650Chessing234 wants to merge 1 commit into
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The statement read
∃ M, ∀ n, ∀ x ∈ Set.Icc 0 1, |f n x| ≤ M ∧
(pointwise convergence) ∧ (each fₙ Riemann integrable) ∧ (F not)
so `∀ n, ∀ x ∈ Icc 0 1` binds the whole conjunction, not just the
bound `|f n x| ≤ M`. The three later conjuncts mention neither `n` nor
that `x`, so each is re-asserted once per pair -- and the `∀ n` is
shadowed by the `∀ n` inside the third conjunct.
Modulo `ℕ` and `Icc 0 1` being nonempty this is equivalent to the
intended statement, so nothing is proved or unproved by the change; it
just stops the reader having to check that equivalence to see what the
exercise asks.
Parenthesise the bound as its own conjunct, matching how Exercise 1.2.2'
directly below already writes the same hypothesis.
This was referenced Aug 15, 2026
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Exercise 1.2.2 currently reads
∧binds tighter than the preceding binders, so∀ n, ∀ x ∈ Icc 0 1scopes overthe entire four-way conjunction rather than over
|f n x| ≤ Malone. The threelater conjuncts mention neither
nnor thatx— the second rebinds its ownx, the third rebinds its ownn, shadowing the outer one — so each isre-asserted once per
(n, x)pair.Since
ℕandIcc 0 1are both nonempty this is equivalent to the intendedstatement, so nothing becomes provable or unprovable here. The cost is only that
a reader has to notice that equivalence before they can see what the exercise is
asking, and the shadowed
∀ ninvites a misreading of the third conjunct.The fix parenthesises the boundedness hypothesis as its own conjunct, which is
how Exercise 1.2.2' immediately below already writes exactly the same hypothesis:
so the two neighbouring statements now agree on the shape of the shared
hypothesis.
Independent of #649, which touches Exercise 1.2.2' a few lines below; the changed
lines are disjoint, so the two merge in either order.
No Lean toolchain build was run for this — relying on the build CI on this PR.