# from the theory of proveit.linear_algebra.vector_sets¶

In [1]:
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.
# import Expression classes needed to build the expression
from proveit import Conditional, V, n
from proveit.core_expr_types import x_1_to_n
from proveit.linear_algebra import Bases, Dim
from proveit.logic import Equals, Forall, InSet, Set
from proveit.numbers import NaturalPos
In [2]:
# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [x_1_to_n], instance_expr = Equals(Dim(V), n), condition = InSet(Set(x_1_to_n), Bases(V))), InSet(n, NaturalPos))
expr:
In [3]:
# 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
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\left\{\forall_{x_{1}, x_{2}, \ldots, x_{n}~|~\left\{x_{1}, x_{2}, \ldots, x_{n}\right\} \in \textrm{Bases}\left(V\right)}~\left(\textrm{Dim}\left(V\right) = n\right) \textrm{ if } n \in \mathbb{N}^+\right..
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()
core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 3
operand: 6
2Operationoperator: 13
operands: 5
3Literal
4ExprTuple6
5ExprTuple27, 7
6Lambdaparameters: 20
body: 8
7Literal
8Conditionalvalue: 9
condition: 10
9Operationoperator: 11
operands: 12
10Operationoperator: 13
operands: 14
11Literal
12ExprTuple15, 27
13Literal
14ExprTuple16, 17
15Operationoperator: 18
operand: 24
16Operationoperator: 19
operands: 20
17Operationoperator: 21
operand: 24
18Literal
19Literal
20ExprTuple23
21Literal
22ExprTuple24
23ExprRangelambda_map: 25
start_index: 26
end_index: 27
24Variable
25Lambdaparameter: 31
body: 28
26Literal
27Variable
28IndexedVarvariable: 29
index: 31
29Variable
30ExprTuple31
31Variable