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 Span, SpanningSets
from proveit.logic import And, Equals, InSet, 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, SpanningSets(V)), Equals(V, Span(sub_expr2))), 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\{\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) \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: 26 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 11 operands: 4
3	Operation	operator: 5 operands: 6
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9
7	Operation	operator: 21 operands: 10
8	Operation	operator: 11 operands: 12
9	ExprRange	lambda_map: 13 start_index: 29 end_index: 30
10	ExprTuple	23, 14
11	Literal
12	ExprTuple	24, 15
13	Lambda	parameter: 34 body: 16
14	Operation	operator: 17 operand: 24
15	Operation	operator: 19 operand: 23
16	Operation	operator: 21 operands: 22
17	Literal
18	ExprTuple	24
19	Literal
20	ExprTuple	23
21	Literal
22	ExprTuple	31, 24
23	Operation	operator: 25 operands: 26
24	Variable
25	Literal
26	ExprTuple	27
27	ExprRange	lambda_map: 28 start_index: 29 end_index: 30
28	Lambda	parameter: 34 body: 31
29	Literal
30	Variable
31	IndexedVar	variable: 32 index: 34
32	Variable
33	ExprTuple	34
34	Variable