Expression of type Equals

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, x_1_to_n
from proveit.linear_algebra import Span, lin_comb_axn
from proveit.logic import Equals, Set, SetOfAll

# build up the expression from sub-expressions
expr = Equals(Span(Set(x_1_to_n)), SetOfAll(instance_param_or_params = [a_1_to_n], instance_element = lin_comb_axn, domain = K)).with_wrapping_at(2)

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())

\begin{array}{c} \begin{array}{l} \textrm{Span}\left(\left\{x_{1}, x_{2}, \ldots, x_{n}\right\}\right) =  \\ \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} \end{array} \end{array}

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	(2)	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operand: 10
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	10
9	Operation	operator: 11 operands: 12
10	Lambda	parameters: 13 body: 14
11	Literal
12	ExprTuple	15
13	ExprTuple	16
14	Conditional	value: 17 condition: 18
15	ExprRange	lambda_map: 19 start_index: 29 end_index: 30
16	ExprRange	lambda_map: 20 start_index: 29 end_index: 30
17	Operation	operator: 21 operands: 22
18	Operation	operator: 23 operands: 24
19	Lambda	parameter: 43 body: 37
20	Lambda	parameter: 43 body: 38
21	Literal
22	ExprTuple	25
23	Literal
24	ExprTuple	26
25	ExprRange	lambda_map: 27 start_index: 29 end_index: 30
26	ExprRange	lambda_map: 28 start_index: 29 end_index: 30
27	Lambda	parameter: 43 body: 31
28	Lambda	parameter: 43 body: 32
29	Literal
30	Variable
31	Operation	operator: 33 operands: 34
32	Operation	operator: 35 operands: 36
33	Literal
34	ExprTuple	38, 37
35	Literal
36	ExprTuple	38, 39
37	IndexedVar	variable: 40 index: 43
38	IndexedVar	variable: 41 index: 43
39	Variable
40	Variable
41	Variable
42	ExprTuple	43
43	Variable