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, K, Lambda, V, n
from proveit.core_expr_types import x_1_to_n
from proveit.linear_algebra import Bases, Dim, VecSpaces
from proveit.logic import Equals, Forall, InClass, InSet, Set
from proveit.numbers import NaturalPos

In [2]:
# build up the expression from sub-expressions
expr = Lambda(V, Conditional(Forall(instance_param_or_params = [n], instance_expr = Forall(instance_param_or_params = [x_1_to_n], instance_expr = Equals(Dim(V), n), condition = InSet(Set(x_1_to_n), Bases(V))), domain = NaturalPos), InClass(V, VecSpaces(K))))

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())

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

In [5]:
stored_expr.style_options()

no style options
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Lambdaparameter: 37
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 16
operand: 7
3Operationoperator: 5
operands: 6
4ExprTuple7
5Literal
6ExprTuple37, 8
7Lambdaparameter: 40
body: 10
8Operationoperator: 11
operand: 15
9ExprTuple40
10Conditionalvalue: 13
condition: 14
11Literal
12ExprTuple15
13Operationoperator: 16
operand: 19
14Operationoperator: 26
operands: 18
15Variable
16Literal
17ExprTuple19
18ExprTuple40, 20
19Lambdaparameters: 33
body: 21
20Literal
21Conditionalvalue: 22
condition: 23
22Operationoperator: 24
operands: 25
23Operationoperator: 26
operands: 27
24Literal
25ExprTuple28, 40
26Literal
27ExprTuple29, 30
28Operationoperator: 31
operand: 37
29Operationoperator: 32
operands: 33
30Operationoperator: 34
operand: 37
31Literal
32Literal
33ExprTuple36
34Literal
35ExprTuple37
36ExprRangelambda_map: 38
start_index: 39
end_index: 40
37Variable
38Lambdaparameter: 44
body: 41
39Literal
40Variable
41IndexedVarvariable: 42
index: 44
42Variable
43ExprTuple44
44Variable