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Expression of type Lambda

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.
%load_expr # Load the stored expression as 'stored_expr'
# 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 Complex, NaturalPos
In [2]:
# build up the expression from sub-expressions
expr = Lambda(n, Conditional(InClass(CartExp(Complex, n), InnerProdSpaces(Complex)), InSet(n, NaturalPos)))
Out[2]:
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{C}^{n} \underset{{\scriptscriptstyle c}}{\in} \textrm{InnerProdSpaces}\left(\mathbb{C}\right) \textrm{ if } n \in \mathbb{N}^+\right..
In [5]:
stored_expr.style_options()
Out[5]:
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
Out[6]:
 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