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Nits in Chapter 06 "Discrete Mathematics" #301

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Nits in Chapter 06 "Discrete Mathematics" #301

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057dcb4
avoid deprecated notation ∑ i in s
yannickseurin Jun 13, 2025
7c27a4d
replace Nat with ℕ
yannickseurin Jun 13, 2025
2b08ff4
simplify exercise solution
yannickseurin Jun 13, 2025
effc27b
simplify exercise solution
yannickseurin Jun 13, 2025
197c7fd
typo
yannickseurin Jun 16, 2025
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11 changes: 5 additions & 6 deletions MIL/C06_Discrete_Mathematics/S02_Counting_Arguments.lean
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Expand Up @@ -117,7 +117,7 @@ example (n : ℕ) : #(triangle n) = (n + 1) * n / 2 := by
intro x _ y _ xney
simp [disjoint_iff_ne, xney]
-- continue the calculation
transitivity (∑ i in range (n+1), i)
transitivity (∑ i ∈ range (n+1), i)
· congr; ext i
rw [card_image_of_injective, card_range]
intros i1 i2; simp
Expand Down Expand Up @@ -236,7 +236,7 @@ example (n : ℕ) : #(triangle' n) = #(triangle n) := by
omega
. simp; omega
rw [this, card_image_of_injOn]
rintro ⟨p1, p2⟩ hp ⟨q1, q2⟩ hq; simp [f] at *
rintro ⟨p1, p2⟩ hp ⟨q1, q2⟩ hq; simp [f]
BOTH: -/
-- QUOTE.

Expand All @@ -253,7 +253,7 @@ EXAMPLES: -/
section
-- QUOTE:
open Classical
variable (s t : Finset Nat) (a b : Nat)
variable (s t : Finset ℕ) (a b : ℕ)

theorem doubleCounting {α β : Type*} (s : Finset α) (t : Finset β)
(r : α → β → Prop)
Expand Down Expand Up @@ -313,9 +313,8 @@ BOTH: -/
sorry
/- SOLUTIONS:
rcases ht' with ⟨m, ⟨hm, hm'⟩, k, ⟨hk, hk'⟩, hmk⟩
use m, hm, k, hk
have : m = k + 1 ∨ k = m + 1 := by omega
rcases this with rfl | rfl
. use k, hk, k+1, hm; simp
. use m, hm, m+1, hk; simp
rcases this with h | h <;> simp [h]
BOTH: -/
-- QUOTE.
2 changes: 1 addition & 1 deletion MIL/C06_Discrete_Mathematics/S03_Inductive_Structures.lean
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Expand Up @@ -131,7 +131,7 @@ linear-time implementation.
Try proving ``reverse (as ++ bs) = reverse bs ++ reverse as`` and
``reverse (reverse as) = as``.
You can use ``cons_append`` and ``append_assoc``, but you
You may need to come up with auxiliary lemmas and prove them.
may need to come up with auxiliary lemmas and prove them.
EXAMPLES: -/
-- QUOTE:
def reverseαα : List α → List α := sorry
Expand Down