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, c, d, k, m, n
from proveit.core_expr_types import b_1_to_n
from proveit.logic import And, Equals, InSet
from proveit.numbers import Add, DecimalSequence, Digits, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(a, sub_expr1)
sub_expr3 = IndexedVar(d, sub_expr1)
sub_expr4 = ExprRange(sub_expr1, sub_expr2, one, m)
sub_expr5 = ExprRange(sub_expr1, sub_expr3, one, k)
sub_expr6 = Add(b_1_to_n)
expr = Conditional(Equals(DecimalSequence(sub_expr4, sub_expr6, sub_expr5), DecimalSequence(sub_expr4, c, sub_expr5)), And(ExprRange(sub_expr1, InSet(sub_expr2, Digits), one, m), ExprRange(sub_expr1, InSet(IndexedVar(b, sub_expr1), Digits), one, n), InSet(c, Digits), ExprRange(sub_expr1, InSet(sub_expr3, Digits), one, k), Equals(sub_expr6, c)))

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\{\texttt{\#}(a_{1}, a_{2}, \ldots, a_{m} ~ \left(b_{1} +  b_{2} +  \ldots +  b_{n}\right) ~ d_{1}, d_{2}, \ldots, d_{k}) = \texttt{\#}(a_{1}, a_{2}, \ldots, a_{m} ~ c ~ d_{1}, d_{2}, \ldots, d_{k}) \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), \left(b_{1} \in \mathbb{N}^{\leq 9}\right) ,  \left(b_{2} \in \mathbb{N}^{\leq 9}\right) ,  \ldots ,  \left(b_{n} \in \mathbb{N}^{\leq 9}\right) ,  c \in \mathbb{N}^{\leq 9}, \left(d_{1} \in \mathbb{N}^{\leq 9}\right) ,  \left(d_{2} \in \mathbb{N}^{\leq 9}\right) ,  \ldots ,  \left(d_{k} \in \mathbb{N}^{\leq 9}\right) ,  \left(b_{1} +  b_{2} +  \ldots +  b_{n}\right) = c\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: 20 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	8, 9, 10, 11, 12
6	Operation	operator: 14 operands: 13
7	Operation	operator: 14 operands: 15
8	ExprRange	lambda_map: 16 start_index: 46 end_index: 30
9	ExprRange	lambda_map: 17 start_index: 46 end_index: 47
10	Operation	operator: 35 operands: 18
11	ExprRange	lambda_map: 19 start_index: 46 end_index: 32
12	Operation	operator: 20 operands: 21
13	ExprTuple	22, 27, 23
14	Literal
15	ExprTuple	22, 28, 23
16	Lambda	parameter: 51 body: 24
17	Lambda	parameter: 51 body: 25
18	ExprTuple	28, 41
19	Lambda	parameter: 51 body: 26
20	Literal
21	ExprTuple	27, 28
22	ExprRange	lambda_map: 29 start_index: 46 end_index: 30
23	ExprRange	lambda_map: 31 start_index: 46 end_index: 32
24	Operation	operator: 35 operands: 33
25	Operation	operator: 35 operands: 34
26	Operation	operator: 35 operands: 36
27	Operation	operator: 37 operands: 38
28	Variable
29	Lambda	parameter: 51 body: 39
30	Variable
31	Lambda	parameter: 51 body: 40
32	Variable
33	ExprTuple	39, 41
34	ExprTuple	48, 41
35	Literal
36	ExprTuple	40, 41
37	Literal
38	ExprTuple	42
39	IndexedVar	variable: 43 index: 51
40	IndexedVar	variable: 44 index: 51
41	Literal
42	ExprRange	lambda_map: 45 start_index: 46 end_index: 47
43	Variable
44	Variable
45	Lambda	parameter: 51 body: 48
46	Literal
47	Variable
48	IndexedVar	variable: 49 index: 51
49	Variable
50	ExprTuple	51
51	Variable