Expression of type Conditional

from the theory of proveit.linear_algebra.addition

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, 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

# build up the expression from sub-expressions
expr = 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:

# 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

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\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..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 16 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	8, 9, 10
6	Operation	operator: 41 operand: 18
7	Operation	operator: 35 operands: 12
8	Operation	operator: 14 operands: 13
9	Operation	operator: 14 operands: 15
10	Operation	operator: 16 operands: 17
11	ExprTuple	18
12	ExprTuple	19, 20
13	ExprTuple	43, 21
14	Literal
15	ExprTuple	44, 21
16	Literal
17	ExprTuple	22, 23
18	Operation	operator: 24 operands: 30
19	Operation	operator: 25 operands: 26
20	Operation	operator: 27 operands: 28
21	Variable
22	Operation	operator: 29 operands: 30
23	Literal
24	Literal
25	Literal
26	ExprTuple	31, 32
27	Literal
28	ExprTuple	33, 39
29	Literal
30	ExprTuple	43, 44
31	Operation	operator: 35 operands: 34
32	Operation	operator: 35 operands: 36
33	Literal
34	ExprTuple	37, 39
35	Literal
36	ExprTuple	38, 39
37	Operation	operator: 41 operand: 43
38	Operation	operator: 41 operand: 44
39	Literal
40	ExprTuple	43
41	Literal
42	ExprTuple	44
43	Variable
44	Variable