Expression of type Conditional

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 Conditional, V, n
from proveit.core_expr_types import x_1_to_n
from proveit.linear_algebra import Bases, Dim
from proveit.logic import Equals, InSet, Set

# build up the expression from sub-expressions
expr = Conditional(Equals(Dim(V), n), InSet(Set(x_1_to_n), Bases(V)))

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\{\textrm{Dim}\left(V\right) = n \textrm{ if } \left\{x_{1}, x_{2}, \ldots, x_{n}\right\} \in \textrm{Bases}\left(V\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, 19
5	Literal
6	ExprTuple	8, 9
7	Operation	operator: 10 operand: 16
8	Operation	operator: 11 operands: 12
9	Operation	operator: 13 operand: 16
10	Literal
11	Literal
12	ExprTuple	15
13	Literal
14	ExprTuple	16
15	ExprRange	lambda_map: 17 start_index: 18 end_index: 19
16	Variable
17	Lambda	parameter: 23 body: 20
18	Literal
19	Variable
20	IndexedVar	variable: 21 index: 23
21	Variable
22	ExprTuple	23
23	Variable