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 V
from proveit.core_expr_types import x_1_to_n
from proveit.linear_algebra import Span, SpanningSets
from proveit.logic import Equals, InSet, Set

# build up the expression from sub-expressions
sub_expr1 = Set(x_1_to_n)
expr = Equals(InSet(sub_expr1, SpanningSets(V)), Equals(V, Span(sub_expr1)))

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\{x_{1}, x_{2}, \ldots, x_{n}\right\} \in \textrm{SpanningSets}\left(V\right)\right) = \left(V = \textrm{Span}\left(\left\{x_{1}, x_{2}, \ldots, x_{n}\right\}\right)\right)

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.	()	()	('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: 6 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	15, 8
6	Literal
7	ExprTuple	14, 9
8	Operation	operator: 10 operand: 14
9	Operation	operator: 12 operand: 15
10	Literal
11	ExprTuple	14
12	Literal
13	ExprTuple	15
14	Variable
15	Operation	operator: 16 operands: 17
16	Literal
17	ExprTuple	18
18	ExprRange	lambda_map: 19 start_index: 20 end_index: 21
19	Lambda	parameter: 25 body: 22
20	Literal
21	Variable
22	IndexedVar	variable: 23 index: 25
23	Variable
24	ExprTuple	25
25	Variable