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, IndexedVar, Variable, a, b, k, m
from proveit.logic import And, Equals, InSet
from proveit.numbers import Add, DecimalSequence, Digits, Less, nine, one, zero

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(a, sub_expr1)
sub_expr3 = ExprRange(sub_expr1, sub_expr2, one, m)
expr = Conditional(Equals(Add(DecimalSequence(sub_expr3, b, ExprRange(sub_expr1, nine, one, k)), one), DecimalSequence(sub_expr3, Add(b, one), ExprRange(sub_expr1, zero, one, k))), And(ExprRange(sub_expr1, InSet(sub_expr2, Digits), one, m), InSet(b, Digits), Less(b, nine)))

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{\#}(a_{1}, a_{2}, \ldots, a_{m} ~ b ~ 9, 9, ..\left(k - 3\right) \times.., 9) + 1\right) = \texttt{\#}(a_{1}, a_{2}, \ldots, a_{m} ~ \left(b + 1\right) ~ 0, 0, ..\left(k - 3\right) \times.., 0) \textrm{ if } \left(a_{1} \in \mathbb{N}^{\leq 9}\right) ,  \left(a_{2} \in \mathbb{N}^{\leq 9}\right) ,  \ldots ,  \left(a_{m} \in \mathbb{N}^{\leq 9}\right) ,  b \in \mathbb{N}^{\leq 9} ,  b < 9\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	9, 10, 11
7	Operation	operator: 24 operands: 12
8	Operation	operator: 22 operands: 13
9	ExprRange	lambda_map: 14 start_index: 37 end_index: 35
10	Operation	operator: 27 operands: 15
11	Operation	operator: 16 operands: 17
12	ExprTuple	18, 37
13	ExprTuple	29, 19, 20
14	Lambda	parameter: 43 body: 21
15	ExprTuple	31, 33
16	Literal
17	ExprTuple	31, 40
18	Operation	operator: 22 operands: 23
19	Operation	operator: 24 operands: 25
20	ExprRange	lambda_map: 26 start_index: 37 end_index: 38
21	Operation	operator: 27 operands: 28
22	Literal
23	ExprTuple	29, 31, 30
24	Literal
25	ExprTuple	31, 37
26	Lambda	parameter: 43 body: 32
27	Literal
28	ExprTuple	39, 33
29	ExprRange	lambda_map: 34 start_index: 37 end_index: 35
30	ExprRange	lambda_map: 36 start_index: 37 end_index: 38
31	Variable
32	Literal
33	Literal
34	Lambda	parameter: 43 body: 39
35	Variable
36	Lambda	parameter: 43 body: 40
37	Literal
38	Variable
39	IndexedVar	variable: 41 index: 43
40	Literal
41	Variable
42	ExprTuple	43
43	Variable