# IoI is transport #641

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merged 2 commits into from Oct 14, 2014

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### mikeshulman commented Mar 2, 2014

 Did we really not ever mention explicitly that these are the same?
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 bump

### EgbertRijke reviewed Oct 14, 2014

 @@ -1655,7 +1655,7 @@ \subsection{Path induction} \[ \indid{A}(C,c,x,x,\refl{x}) \defeq c(x). \] The function \$ \indid{A}\$ is traditionally called \$J\$. \indexsee{J@\$J\$}{induction principle for identity type}% -We leave it as an easy exercise to show that indiscernability of identicals follows from path induction. +It as an easy exercise to show that indiscernability of identicals follows from path induction; we will do this in \autoref{lem:transport}, where we will also give a new name and notation for indiscernability of identicals.

#### EgbertRijke Oct 14, 2014

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There's a typo: "It as" should read "It is"

#### EgbertRijke Oct 14, 2014

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Since we prove IoI as a lemma, why don't we skip the "exercise" and rephrase this sentence as: "We will show in \autoref{lem:transport} that indiscernability of identicals is an instance of path induction. There we will also give a new name and notation for indiscernability of identicals."

This way we also tell why it is easy, because it is a special case.

### mikeshulman added some commits Mar 2, 2014

``` IoI is transport ```
``` cca7574 ```
``` better wording for ioi is transport ```
``` 924a0ff ```
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### mikeshulman commented Oct 14, 2014

 @EgbertRijke, thanks for the suggestions; fixed (and also rebased against master, since so much time has passed since this was submitted, e.g. `autoref` -> `cref` happened).

### andrejbauer added a commit that referenced this pull request Oct 14, 2014

``` Merge pull request #641 from mikeshulman/ioi-is-transport ```
`IoI is transport`
``` 354bc0a ```

### andrejbauer merged commit `354bc0a` into HoTT:master Oct 14, 2014 1 check passed

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