Expression of type ExprTuple

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, ExprTuple, Lambda, 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 = ExprTuple(Lambda(k, 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(k \mapsto \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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 25 body: 3
2	ExprTuple	25
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	25, 12
10	Operation	operator: 13 operands: 14
11	Operation	operator: 18 operands: 15
12	Literal
13	Literal
14	ExprTuple	16, 24
15	ExprTuple	24, 17
16	Operation	operator: 18 operands: 19
17	ExprRange	lambda_map: 20 start_index: 24 end_index: 25
18	Literal
19	ExprTuple	21
20	Lambda	parameter: 28 body: 22
21	ExprRange	lambda_map: 23 start_index: 24 end_index: 25
22	Literal
23	Lambda	parameter: 28 body: 27
24	Literal
25	Variable
26	ExprTuple	28
27	Literal
28	Variable