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 Span, SpanningSets
from proveit.logic import Equals, Forall, InSet, Set
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
sub_expr1 = Set(x_1_to_n)
expr = ExprTuple(Lambda(n, Conditional(Forall(instance_param_or_params = [x_1_to_n], instance_expr = Equals(InSet(sub_expr1, SpanningSets(V)), Equals(V, Span(sub_expr1))), domain = V).with_wrapping(), InSet(n, NaturalPos))))

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(n \mapsto \left\{\begin{array}{l}\forall_{x_{1}, x_{2}, \ldots, x_{n} \in V}~\\
\left(\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)\right)\end{array} \textrm{ if } n \in \mathbb{N}^+\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	parameter: 40 body: 3
2	ExprTuple	40
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 31 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	40, 10
9	Lambda	parameters: 36 body: 11
10	Literal
11	Conditional	value: 12 condition: 13
12	Operation	operator: 21 operands: 14
13	Operation	operator: 15 operands: 16
14	ExprTuple	17, 18
15	Literal
16	ExprTuple	19
17	Operation	operator: 31 operands: 20
18	Operation	operator: 21 operands: 22
19	ExprRange	lambda_map: 23 start_index: 39 end_index: 40
20	ExprTuple	33, 24
21	Literal
22	ExprTuple	34, 25
23	Lambda	parameter: 44 body: 26
24	Operation	operator: 27 operand: 34
25	Operation	operator: 29 operand: 33
26	Operation	operator: 31 operands: 32
27	Literal
28	ExprTuple	34
29	Literal
30	ExprTuple	33
31	Literal
32	ExprTuple	41, 34
33	Operation	operator: 35 operands: 36
34	Variable
35	Literal
36	ExprTuple	37
37	ExprRange	lambda_map: 38 start_index: 39 end_index: 40
38	Lambda	parameter: 44 body: 41
39	Literal
40	Variable
41	IndexedVar	variable: 42 index: 44
42	Variable
43	ExprTuple	44
44	Variable