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Fix: ambiguity with newly introduced divisibility symbol #108

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Fix: ambiguity with newly introduced divisibility symbol #108

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7075dae
fixed divides symbol ambiguity
MatteoGaetzner Mar 10, 2024
184d3b6
improved divisibility documentation
MatteoGaetzner Mar 10, 2024
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12 changes: 5 additions & 7 deletions quantifiers_and_equality.md
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Original file line number Diff line number Diff line change
Expand Up @@ -497,20 +497,18 @@ example (h₁ : divides x y) (h₂ : y = z) : divides x (2*z) :=
_ = z := h₂
divides _ (2*z) := divides_mul ..

infix:50 " ∣ " => divides
infix:51 " ‖ " => divides

example (h₁ : divides x y) (h₂ : y = z) : divides x (2*z) :=
calc
x ∣ y := h₁
x ‖ y := h₁
_ = z := h₂
_ ∣ 2*z := divides_mul ..
_ ‖ 2*z := divides_mul ..
```

The example above also makes it clear that you can use `calc` even if you
do not have an infix notation for your relation. Finally we remark that
the vertical bar `∣` in the example above is the unicode one. We use
unicode to make sure we do not overload the ASCII `|` used in the
`match .. with` expression.
do not have an infix notation for your relation.
Finally, we remark that, in the example above, we use the double pipe `‖` symbol instead of the vertical bar `∣` or ASCII `|`. We do that to avoid ambiguity with the already defined `∣` and overloading `|` used in the `match .. with` expression. In practice, it is probably better to use the standard library's `∣` (or `Dvd.dvd`) to express divisibility instead of defining it yourself.

With ``calc``, we can write the proof in the last section in a more
natural and perspicuous way.
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