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Mirrors > Home > ILE Home > Th. List > df-oexpi | Unicode version |
Description: Define the ordinal
exponentiation operation.
This definition is similar to a conventional definition of
exponentiation except that it defines We do not yet have an extensive development of ordinal exponentiation. For background on ordinal exponentiation without excluded middle, see Tom de Jong, Nicolai Kraus, Fredrik Nordvall Forsberg, and Chuangjie Xu (2025), "Ordinal Exponentiation in Homotopy Type Theory", arXiv:2501.14542 , https://arxiv.org/abs/2501.14542 which is formalized in the TypeTopology proof library at https://ordinal-exponentiation-hott.github.io/. (Contributed by Mario Carneiro, 4-Jul-2019.) |
Ref | Expression |
---|---|
df-oexpi |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | coei 6415 |
. 2
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2 | vx |
. . 3
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3 | vy |
. . 3
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4 | con0 4363 |
. . 3
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5 | 3 | cv 1352 |
. . . 4
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6 | vz |
. . . . . 6
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7 | cvv 2737 |
. . . . . 6
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8 | 6 | cv 1352 |
. . . . . . 7
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9 | 2 | cv 1352 |
. . . . . . 7
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10 | comu 6414 |
. . . . . . 7
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11 | 8, 9, 10 | co 5874 |
. . . . . 6
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12 | 6, 7, 11 | cmpt 4064 |
. . . . 5
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13 | c1o 6409 |
. . . . 5
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14 | 12, 13 | crdg 6369 |
. . . 4
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15 | 5, 14 | cfv 5216 |
. . 3
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16 | 2, 3, 4, 4, 15 | cmpo 5876 |
. 2
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17 | 1, 16 | wceq 1353 |
1
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Colors of variables: wff set class |
This definition is referenced by: fnoei 6452 oeiexg 6453 oeiv 6456 |
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