Expression of type SetOfAll

from the theory of proveit.linear_algebra.vector_sets

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 K
from proveit.core_expr_types import a_1_to_n
from proveit.linear_algebra import lin_comb_axn
from proveit.logic import SetOfAll

# build up the expression from sub-expressions
expr = SetOfAll(instance_param_or_params = [a_1_to_n], instance_element = lin_comb_axn, domain = K)

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} \cdot x_{1}\right) +  \left(a_{2} \cdot x_{2}\right) +  \ldots +  \left(a_{n} \cdot x_{n}\right)\right\}_{a_{1}, a_{2}, \ldots, a_{n} \in K}

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameters: 4 body: 5
4	ExprTuple	6
5	Conditional	value: 7 condition: 8
6	ExprRange	lambda_map: 9 start_index: 18 end_index: 19
7	Operation	operator: 10 operands: 11
8	Operation	operator: 12 operands: 13
9	Lambda	parameter: 32 body: 27
10	Literal
11	ExprTuple	14
12	Literal
13	ExprTuple	15
14	ExprRange	lambda_map: 16 start_index: 18 end_index: 19
15	ExprRange	lambda_map: 17 start_index: 18 end_index: 19
16	Lambda	parameter: 32 body: 20
17	Lambda	parameter: 32 body: 21
18	Literal
19	Variable
20	Operation	operator: 22 operands: 23
21	Operation	operator: 24 operands: 25
22	Literal
23	ExprTuple	27, 26
24	Literal
25	ExprTuple	27, 28
26	IndexedVar	variable: 29 index: 32
27	IndexedVar	variable: 30 index: 32
28	Variable
29	Variable
30	Variable
31	ExprTuple	32
32	Variable