Expression of type Lambda

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, Lambda, V, n
from proveit.core_expr_types import x_1_to_n
from proveit.linear_algebra import Bases, LinDepSets, SpanningSets
from proveit.logic import And, Equals, Forall, InSet, NotInSet, Set
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
sub_expr1 = Set(x_1_to_n)
expr = Lambda(n, Conditional(Forall(instance_param_or_params = [x_1_to_n], instance_expr = Equals(InSet(sub_expr1, Bases(V)), And(InSet(sub_expr1, SpanningSets(V)), NotInSet(sub_expr1, LinDepSets(V))).with_wrapping_at(2)).with_wrapping_at(2), 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())

n \mapsto \left\{\begin{array}{l}\forall_{x_{1}, x_{2}, \ldots, x_{n} \in V}~\\
\left(\begin{array}{c} \begin{array}{l} \left(\left\{x_{1}, x_{2}, \ldots, x_{n}\right\} \in \textrm{Bases}\left(V\right)\right) =  \\ \left(\begin{array}{c} \left(\left\{x_{1}, x_{2}, \ldots, x_{n}\right\} \in \textrm{SpanningSets}\left(V\right)\right) \land  \\ \left(\left\{x_{1}, x_{2}, \ldots, x_{n}\right\} \notin \textrm{LinDepSets}\left(V\right)\right) \end{array}\right) \end{array} \end{array}\right)\end{array} \textrm{ if } n \in \mathbb{N}^+\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 45 body: 2
1	ExprTuple	45
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 31 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	45, 9
8	Lambda	parameters: 38 body: 10
9	Literal
10	Conditional	value: 11 condition: 12
11	Operation	operator: 13 operands: 14
12	Operation	operator: 20 operands: 15
13	Literal
14	ExprTuple	16, 17
15	ExprTuple	18
16	Operation	operator: 31 operands: 19
17	Operation	operator: 20 operands: 21
18	ExprRange	lambda_map: 22 start_index: 44 end_index: 45
19	ExprTuple	34, 23
20	Literal
21	ExprTuple	24, 25
22	Lambda	parameter: 49 body: 26
23	Operation	operator: 27 operand: 42
24	Operation	operator: 31 operands: 28
25	Operation	operator: 29 operands: 30
26	Operation	operator: 31 operands: 32
27	Literal
28	ExprTuple	34, 33
29	Literal
30	ExprTuple	34, 35
31	Literal
32	ExprTuple	46, 42
33	Operation	operator: 36 operand: 42
34	Operation	operator: 37 operands: 38
35	Operation	operator: 39 operand: 42
36	Literal
37	Literal
38	ExprTuple	41
39	Literal
40	ExprTuple	42
41	ExprRange	lambda_map: 43 start_index: 44 end_index: 45
42	Variable
43	Lambda	parameter: 49 body: 46
44	Literal
45	Variable
46	IndexedVar	variable: 47 index: 49
47	Variable
48	ExprTuple	49
49	Variable