Expression of type Lambda

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, 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 = 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())

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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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