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 K, Lambda, V, n
from proveit.core_expr_types import x_1_to_n
from proveit.linear_algebra import Bases, LinDepSets, SpanningSets, VecSpaces
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(K, Forall(instance_param_or_params = [V], instance_expr = Forall(instance_param_or_params = [n], instance_expr = 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(), domain = NaturalPos), domain = VecSpaces(K)))

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())

K \mapsto \left[\forall_{V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\left[\forall_{n \in \mathbb{N}^+}~\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}\right]\right]\right]

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 18 body: 1
1	Operation	operator: 19 operand: 3
2	ExprTuple	3
3	Lambda	parameter: 56 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 19 operand: 10
6	Operation	operator: 8 operands: 9
7	ExprTuple	10
8	Literal
9	ExprTuple	56, 11
10	Lambda	parameter: 59 body: 13
11	Operation	operator: 14 operand: 18
12	ExprTuple	59
13	Conditional	value: 16 condition: 17
14	Literal
15	ExprTuple	18
16	Operation	operator: 19 operand: 22
17	Operation	operator: 45 operands: 21
18	Variable
19	Literal
20	ExprTuple	22
21	ExprTuple	59, 23
22	Lambda	parameters: 52 body: 24
23	Literal
24	Conditional	value: 25 condition: 26
25	Operation	operator: 27 operands: 28
26	Operation	operator: 34 operands: 29
27	Literal
28	ExprTuple	30, 31
29	ExprTuple	32
30	Operation	operator: 45 operands: 33
31	Operation	operator: 34 operands: 35
32	ExprRange	lambda_map: 36 start_index: 58 end_index: 59
33	ExprTuple	48, 37
34	Literal
35	ExprTuple	38, 39
36	Lambda	parameter: 63 body: 40
37	Operation	operator: 41 operand: 56
38	Operation	operator: 45 operands: 42
39	Operation	operator: 43 operands: 44
40	Operation	operator: 45 operands: 46
41	Literal
42	ExprTuple	48, 47
43	Literal
44	ExprTuple	48, 49
45	Literal
46	ExprTuple	60, 56
47	Operation	operator: 50 operand: 56
48	Operation	operator: 51 operands: 52
49	Operation	operator: 53 operand: 56
50	Literal
51	Literal
52	ExprTuple	55
53	Literal
54	ExprTuple	56
55	ExprRange	lambda_map: 57 start_index: 58 end_index: 59
56	Variable
57	Lambda	parameter: 63 body: 60
58	Literal
59	Variable
60	IndexedVar	variable: 61 index: 63
61	Variable
62	ExprTuple	63
63	Variable