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, Dim
from proveit.logic import Equals, InSet, Set

# build up the expression from sub-expressions
expr = Lambda([x_1_to_n], Conditional(Equals(Dim(V), n), InSet(Set(x_1_to_n), Bases(V))))

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\{\textrm{Dim}\left(V\right) = n \textrm{ if } \left\{x_{1}, x_{2}, \ldots, x_{n}\right\} \in \textrm{Bases}\left(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: 13 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 20
6	Literal
7	ExprTuple	9, 10
8	Operation	operator: 11 operand: 17
9	Operation	operator: 12 operands: 13
10	Operation	operator: 14 operand: 17
11	Literal
12	Literal
13	ExprTuple	16
14	Literal
15	ExprTuple	17
16	ExprRange	lambda_map: 18 start_index: 19 end_index: 20
17	Variable
18	Lambda	parameter: 24 body: 21
19	Literal
20	Variable
21	IndexedVar	variable: 22 index: 24
22	Variable
23	ExprTuple	24
24	Variable