# from the theory of proveit.linear_algebra.inner_products¶

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, ExprTuple, Lambda, n
from proveit.linear_algebra import InnerProdSpaces
from proveit.logic import CartExp, InClass, InSet
from proveit.numbers import NaturalPos, Real

In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda(n, Conditional(InClass(CartExp(Real, n), InnerProdSpaces(Real)), 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(n \mapsto \left\{\mathbb{R}^{n} \underset{{\scriptscriptstyle c}}{\in} \textrm{InnerProdSpaces}\left(\mathbb{R}\right) \textrm{ if } n \in \mathbb{N}^+\right..\right)

In [5]:
stored_expr.style_options()

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

core typesub-expressionsexpression
0ExprTuple1
1Lambdaparameter: 17
body: 3
2ExprTuple17
3Conditionalvalue: 4
condition: 5
4Operationoperator: 6
operands: 7
5Operationoperator: 8
operands: 9
6Literal
7ExprTuple10, 11
8Literal
9ExprTuple17, 12
10Operationoperator: 13
operands: 14
11Operationoperator: 15
operand: 18
12Literal
13Literal
14ExprTuple18, 17
15Literal
16ExprTuple18
17Variable
18Literal