Expression of type ExprTuple

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, ExprTuple, Lambda, 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 = ExprTuple(Lambda([x_1_to_n], 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(\left(x_{1}, x_{2}, \ldots, x_{n}\right) \mapsto \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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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