Expression of type Conditional

from the theory of proveit.numbers.multiplication

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, n, x
from proveit.core_expr_types import a_1_to_n
from proveit.logic import And, Equals, InSet, Set
from proveit.numbers import Add, Mult, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(Equals(Add(a_1_to_n), Mult(x, n)), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), Set(x)), one, n)))

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(a_{1} +  a_{2} +  \ldots +  a_{n}\right) = \left(x \cdot n\right) \textrm{ if } \left(a_{1} \in \left\{x\right\}\right) \land  \left(a_{2} \in \left\{x\right\}\right) \land  \ldots \land  \left(a_{n} \in \left\{x\right\}\right)\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
7	Operation	operator: 10 operands: 11
8	Operation	operator: 12 operands: 13
9	ExprRange	lambda_map: 14 start_index: 18 end_index: 19
10	Literal
11	ExprTuple	15
12	Literal
13	ExprTuple	29, 19
14	Lambda	parameter: 28 body: 16
15	ExprRange	lambda_map: 17 start_index: 18 end_index: 19
16	Operation	operator: 20 operands: 21
17	Lambda	parameter: 28 body: 22
18	Literal
19	Variable
20	Literal
21	ExprTuple	22, 23
22	IndexedVar	variable: 24 index: 28
23	Operation	operator: 26 operand: 29
24	Variable
25	ExprTuple	28
26	Literal
27	ExprTuple	29
28	Variable
29	Variable