Expression of type Conditional

from the theory of proveit.numbers.numerals.decimals

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, ExprRange, Variable, k
from proveit.logic import Equals, InSet
from proveit.numbers import Add, DecimalSequence, NaturalPos, nine, one, zero

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(Equals(Add(DecimalSequence(ExprRange(sub_expr1, nine, one, k)), one), DecimalSequence(one, ExprRange(sub_expr1, zero, one, k))), InSet(k, NaturalPos))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left\{\left(\texttt{\#}(9, 9, ..\left(k - 3\right) \times.., 9) + 1\right) = \texttt{\#}(1 ~ 0, 0, ..\left(k - 3\right) \times.., 0) \textrm{ if } k \in \mathbb{N}^+\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	22, 9
7	Operation	operator: 10 operands: 11
8	Operation	operator: 15 operands: 12
9	Literal
10	Literal
11	ExprTuple	13, 21
12	ExprTuple	21, 14
13	Operation	operator: 15 operands: 16
14	ExprRange	lambda_map: 17 start_index: 21 end_index: 22
15	Literal
16	ExprTuple	18
17	Lambda	parameter: 25 body: 19
18	ExprRange	lambda_map: 20 start_index: 21 end_index: 22
19	Literal
20	Lambda	parameter: 25 body: 24
21	Literal
22	Variable
23	ExprTuple	25
24	Literal
25	Variable