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Add documentation: Equality, HProp, Isomorphism, Sigma #41

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merged 2 commits into from
Aug 1, 2016

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JasonGross
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As rightly requested by @andres-erbsen

eisadj : forall x : A, eisretr (f x) = ap f (eissect x)
}.
>> *)
(** - Contratible fibers: [∀ y : B, Contr { x : A | f x = y }] where
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Did you mean "contractible"?

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Yes, thanks

@andres-erbsen
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Much appreciated. LGTM as is, but please see whether you can do something about the commented things before you merge.

@JasonGross JasonGross merged commit 212b073 into mit-plv:master Aug 1, 2016
@JasonGross JasonGross deleted the document-HoTT branch August 1, 2016 20:22
JasonGross referenced this pull request in JasonGross/fiat-crypto Feb 21, 2022
Probably if the lists are the same lengths, then we want to compare them
element-wise rather than all at once.  It's way too verbose to keep
expanding them, so we only do that when lists are not the same length.

We now get error messages such as
```
Unable to unify: [inr [378, 381, 384]] == [inr [101, 106, 108]]
Could not unify the values at index 0: [mit-plv#378, mit-plv#381, mit-plv#384] != [mit-plv#101, mit-plv#106, mit-plv#108]
index 0: mit-plv#378 != mit-plv#101
(slice 0 44, [mit-plv#377]) != (slice 0 44, [mit-plv#98])
index 0: mit-plv#377 != mit-plv#98
(add 64, [mit-plv#345, mit-plv#375]) != (add 64, [#57, mit-plv#96])
index 0: mit-plv#345 != #57
(slice 0 44, [mit-plv#337]) != (slice 0 44, [#44])
index 0: mit-plv#337 != #44
(add 64, [#41, mit-plv#334]) != (add 64, [#25, #41])
index 1: mit-plv#334 != #25
(mul 64, [#1, mit-plv#331]) != (mul 64, [#0, #1, #22])
[(add 64, [mit-plv#329, mit-plv#329])] != [#0, (const 20, [])]
[(add 64, [(mul 64, [#7, mit-plv#328]), (mul 64, [#7, mit-plv#328])])] != [#0, (const 20, [])]
[(add 64, [(mul 64, [(const 2, []), (add 64, [#0, mit-plv#327])]), (mul 64, [(const 2, []), (add 64, [#0, mit-plv#327])])])] != [#0, (const 20, [])]
[(add 64, [(mul 64, [(const 2, []), (add 64, [#0, (mul 64, [#0, mit-plv#326])])]), (mul 64, [(const 2, []), (add 64, [#0, (mul 64, [#0, mit-plv#326])])])])] != [#0, (const 20, [])]
[(add 64, [(mul 64, [(const 2, []), (add 64, [#0, (mul 64, [#0, (const 4, [])])])]), (mul 64, [(const 2, []), (add 64, [#0, (mul 64, [#0, (const 4, [])])])])])] != [#0, (const 20, [])]
[(add 64, [(mul 64, [(const 2, []), (add 64, [(old 64 0, []), (mul 64, [(old 64 0, []), (const 4, [])])])]), (mul 64, [(const 2, []), (add 64, [(old 64 0, []), (mul 64, [(old 64 0, []), (const 4, [])])])])])] != [(old 64 0, []), (const 20, [])]
```

The second to last line is generally the one to look at; the last line
adds a bit more detail to it.  Perhaps we should instead list out the
values of indices rather than expanding one additional level?
JasonGross referenced this pull request in JasonGross/fiat-crypto Feb 21, 2022
Probably if the lists are the same lengths, then we want to compare them
element-wise rather than all at once.  It's way too verbose to keep
expanding them, so we only do that when lists are not the same length.

We now get error messages such as
```
Unable to unify: [inr [378, 381, 384]] == [inr [101, 106, 108]]
Could not unify the values at index 0: [mit-plv#378, mit-plv#381, mit-plv#384] != [mit-plv#101, mit-plv#106, mit-plv#108]
index 0: mit-plv#378 != mit-plv#101
(slice 0 44, [mit-plv#377]) != (slice 0 44, [mit-plv#98])
index 0: mit-plv#377 != mit-plv#98
(add 64, [mit-plv#345, mit-plv#375]) != (add 64, [#57, mit-plv#96])
index 0: mit-plv#345 != #57
(slice 0 44, [mit-plv#337]) != (slice 0 44, [#44])
index 0: mit-plv#337 != #44
(add 64, [#41, mit-plv#334]) != (add 64, [#25, #41])
index 1: mit-plv#334 != #25
(mul 64, [#1, mit-plv#331]) != (mul 64, [#0, #1, #22])
[(add 64, [mit-plv#329, mit-plv#329])] != [#0, (const 20, [])]
[(add 64, [(mul 64, [#7, mit-plv#328]), (mul 64, [#7, mit-plv#328])])] != [#0, (const 20, [])]
[(add 64, [(mul 64, [(const 2, []), (add 64, [#0, mit-plv#327])]), (mul 64, [(const 2, []), (add 64, [#0, mit-plv#327])])])] != [#0, (const 20, [])]
[(add 64, [(mul 64, [(const 2, []), (add 64, [#0, (mul 64, [#0, mit-plv#326])])]), (mul 64, [(const 2, []), (add 64, [#0, (mul 64, [#0, mit-plv#326])])])])] != [#0, (const 20, [])]
[(add 64, [(mul 64, [(const 2, []), (add 64, [#0, (mul 64, [#0, (const 4, [])])])]), (mul 64, [(const 2, []), (add 64, [#0, (mul 64, [#0, (const 4, [])])])])])] != [#0, (const 20, [])]
[(add 64, [(mul 64, [(const 2, []), (add 64, [(old 64 0, []), (mul 64, [(old 64 0, []), (const 4, [])])])]), (mul 64, [(const 2, []), (add 64, [(old 64 0, []), (mul 64, [(old 64 0, []), (const 4, [])])])])])] != [(old 64 0, []), (const 20, [])]
```

The second to last line is generally the one to look at; the last line
adds a bit more detail to it.  Perhaps we should instead list out the
values of indices rather than expanding one additional level?
JasonGross added a commit that referenced this pull request Feb 22, 2022
Probably if the lists are the same lengths, then we want to compare them
element-wise rather than all at once.  It's way too verbose to keep
expanding them, so we only do that when lists are not the same length.

We now get error messages such as
```
Unable to unify: [inr [378, 381, 384]] == [inr [101, 106, 108]]
Could not unify the values at index 0: [#378, #381, #384] != [#101, #106, #108]
index 0: #378 != #101
(slice 0 44, [#377]) != (slice 0 44, [#98])
index 0: #377 != #98
(add 64, [#345, #375]) != (add 64, [#57, #96])
index 0: #345 != #57
(slice 0 44, [#337]) != (slice 0 44, [#44])
index 0: #337 != #44
(add 64, [#41, #334]) != (add 64, [#25, #41])
index 1: #334 != #25
(mul 64, [#1, #331]) != (mul 64, [#0, #1, #22])
[(add 64, [#329, #329])] != [#0, (const 20, [])]
[(add 64, [(mul 64, [#7, #328]), (mul 64, [#7, #328])])] != [#0, (const 20, [])]
[(add 64, [(mul 64, [(const 2, []), (add 64, [#0, #327])]), (mul 64, [(const 2, []), (add 64, [#0, #327])])])] != [#0, (const 20, [])]
[(add 64, [(mul 64, [(const 2, []), (add 64, [#0, (mul 64, [#0, #326])])]), (mul 64, [(const 2, []), (add 64, [#0, (mul 64, [#0, #326])])])])] != [#0, (const 20, [])]
[(add 64, [(mul 64, [(const 2, []), (add 64, [#0, (mul 64, [#0, (const 4, [])])])]), (mul 64, [(const 2, []), (add 64, [#0, (mul 64, [#0, (const 4, [])])])])])] != [#0, (const 20, [])]
[(add 64, [(mul 64, [(const 2, []), (add 64, [(old 64 0, []), (mul 64, [(old 64 0, []), (const 4, [])])])]), (mul 64, [(const 2, []), (add 64, [(old 64 0, []), (mul 64, [(old 64 0, []), (const 4, [])])])])])] != [(old 64 0, []), (const 20, [])]
```

The second to last line is generally the one to look at; the last line
adds a bit more detail to it.  Perhaps we should instead list out the
values of indices rather than expanding one additional level?
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