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, ExprRange, IndexedVar, Lambda, V, Variable, n, x
from proveit.core_expr_types import x_1_to_n
from proveit.linear_algebra import Bases, LinDepSets, SpanningSets
from proveit.logic import And, Equals, InSet, NotInSet, Set
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Set(x_1_to_n)
expr = Lambda([x_1_to_n], Conditional(Equals(InSet(sub_expr2, Bases(V)), And(InSet(sub_expr2, SpanningSets(V)), NotInSet(sub_expr2, LinDepSets(V))).with_wrapping_at(2)).with_wrapping_at(2), And(ExprRange(sub_expr1, InSet(IndexedVar(x, sub_expr1), V), one, n))))

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(x_{1}, x_{2}, \ldots, x_{n}\right) \mapsto \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} \textrm{ if } \left(x_{1} \in V\right) \land  \left(x_{2} \in V\right) \land  \ldots \land  \left(x_{n} \in V\right)\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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