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SUPPLEMENTARY MATERIAL (USERS' MATHBOXES)
Mathbox for Alexander van der Vekens
Complexity theory
Digits
0dig1
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0dig2pr01
Metamath Proof Explorer
Ascii
Unicode
Theorem
0dig1
Description:
The
0
th digit of 1 is 1 in any positional system.
(Contributed by
AV
, 28-May-2020)
Ref
Expression
Assertion
0dig1
⊢
B
∈
ℤ
≥
2
→
0
digit
⁡
B
1
=
1
Proof
Step
Hyp
Ref
Expression
1
0z
⊢
0
∈
ℤ
2
dig1
⊢
B
∈
ℤ
≥
2
∧
0
∈
ℤ
→
0
digit
⁡
B
1
=
if
0
=
0
1
0
3
1
2
mpan2
⊢
B
∈
ℤ
≥
2
→
0
digit
⁡
B
1
=
if
0
=
0
1
0
4
eqid
⊢
0
=
0
5
4
iftruei
⊢
if
0
=
0
1
0
=
1
6
3
5
eqtrdi
⊢
B
∈
ℤ
≥
2
→
0
digit
⁡
B
1
=
1