# from the theory of proveit.linear_algebra.addition¶

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, ExprTuple, Lambda, V, a, b
from proveit.linear_algebra import InnerProd, Norm, VecAdd
from proveit.logic import And, Equals, InSet
from proveit.numbers import Add, Exp, sqrt, two, zero

In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda([a, b], Conditional(Equals(Norm(VecAdd(a, b)), sqrt(Add(Exp(Norm(a), two), Exp(Norm(b), two)))), And(InSet(a, V), InSet(b, V), Equals(InnerProd(a, b), zero)))))

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(\left(a, b\right) \mapsto \left\{\left \|a + b\right \| = \sqrt{\left(\left \|a\right \|^{2} + \left \|b\right \|^{2}\right)} \textrm{ if } a \in V ,  b \in V ,  \left \langle a, b\right \rangle = 0\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
1Lambdaparameters: 32
body: 2
2Conditionalvalue: 3
condition: 4
3Operationoperator: 18
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple8, 9
6Literal
7ExprTuple10, 11, 12
8Operationoperator: 43
operand: 20
9Operationoperator: 37
operands: 14
10Operationoperator: 16
operands: 15
11Operationoperator: 16
operands: 17
12Operationoperator: 18
operands: 19
13ExprTuple20
14ExprTuple21, 22
15ExprTuple45, 23
16Literal
17ExprTuple46, 23
18Literal
19ExprTuple24, 25
20Operationoperator: 26
operands: 32
21Operationoperator: 27
operands: 28
22Operationoperator: 29
operands: 30
23Variable
24Operationoperator: 31
operands: 32
25Literal
26Literal
27Literal
28ExprTuple33, 34
29Literal
30ExprTuple35, 41
31Literal
32ExprTuple45, 46
33Operationoperator: 37
operands: 36
34Operationoperator: 37
operands: 38
35Literal
36ExprTuple39, 41
37Literal
38ExprTuple40, 41
39Operationoperator: 43
operand: 45
40Operationoperator: 43
operand: 46
41Literal
42ExprTuple45
43Literal
44ExprTuple46
45Variable
46Variable