# 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, 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 = 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())

n \mapsto \left\{\mathbb{R}^{n} \underset{{\scriptscriptstyle c}}{\in} \textrm{InnerProdSpaces}\left(\mathbb{R}\right) \textrm{ if } n \in \mathbb{N}^+\right..

In [5]:
stored_expr.style_options()

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

core typesub-expressionsexpression
0Lambdaparameter: 16
body: 2
1ExprTuple16
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operands: 6
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9, 10
7Literal
8ExprTuple16, 11
9Operationoperator: 12
operands: 13
10Operationoperator: 14
operand: 17
11Literal
12Literal
13ExprTuple17, 16
14Literal
15ExprTuple17
16Variable
17Literal