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Mirrors > Home > ILE Home > Th. List > df-iexp | Unicode version |
Description: Define exponentiation to
nonnegative integer powers. This definition is
not meant to be used directly; instead, exp0 8913
and expp1 8916 provide the
standard recursive definition. The up-arrow notation is used by Donald
Knuth for iterated exponentiation (Science 194, 1235-1242, 1976)
and
is convenient for us since we don't have superscripts. 10-Jun-2005: The
definition was extended to include zero exponents, so that ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
df-iexp |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cexp 8908 |
. 2
![]() ![]() | |
2 | vx |
. . 3
![]() ![]() | |
3 | vy |
. . 3
![]() ![]() | |
4 | cc 6709 |
. . 3
![]() ![]() | |
5 | cz 8021 |
. . 3
![]() ![]() | |
6 | 3 | cv 1241 |
. . . . 5
![]() ![]() |
7 | cc0 6711 |
. . . . 5
![]() ![]() | |
8 | 6, 7 | wceq 1242 |
. . . 4
![]() ![]() ![]() ![]() |
9 | c1 6712 |
. . . 4
![]() ![]() | |
10 | clt 6857 |
. . . . . 6
![]() ![]() | |
11 | 7, 6, 10 | wbr 3755 |
. . . . 5
![]() ![]() ![]() ![]() |
12 | cmul 6716 |
. . . . . . 7
![]() ![]() | |
13 | cn 7695 |
. . . . . . . 8
![]() ![]() | |
14 | 2 | cv 1241 |
. . . . . . . . 9
![]() ![]() |
15 | 14 | csn 3367 |
. . . . . . . 8
![]() ![]() ![]() ![]() |
16 | 13, 15 | cxp 4286 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
17 | 12, 4, 16, 9 | cseq 8892 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
18 | 6, 17 | cfv 4845 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
19 | 6 | cneg 6980 |
. . . . . . 7
![]() ![]() ![]() |
20 | 19, 17 | cfv 4845 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
21 | cdiv 7433 |
. . . . . 6
![]() ![]() | |
22 | 9, 20, 21 | co 5455 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
23 | 11, 18, 22 | cif 3325 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
24 | 8, 9, 23 | cif 3325 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
25 | 2, 3, 4, 5, 24 | cmpt2 5457 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
26 | 1, 25 | wceq 1242 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
This definition is referenced by: expival 8911 |
Copyright terms: Public domain | W3C validator |