Expression of type ExprTuple

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, 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

# 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:

# 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) \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)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 32 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 18 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 11, 12
8	Operation	operator: 43 operand: 20
9	Operation	operator: 37 operands: 14
10	Operation	operator: 16 operands: 15
11	Operation	operator: 16 operands: 17
12	Operation	operator: 18 operands: 19
13	ExprTuple	20
14	ExprTuple	21, 22
15	ExprTuple	45, 23
16	Literal
17	ExprTuple	46, 23
18	Literal
19	ExprTuple	24, 25
20	Operation	operator: 26 operands: 32
21	Operation	operator: 27 operands: 28
22	Operation	operator: 29 operands: 30
23	Variable
24	Operation	operator: 31 operands: 32
25	Literal
26	Literal
27	Literal
28	ExprTuple	33, 34
29	Literal
30	ExprTuple	35, 41
31	Literal
32	ExprTuple	45, 46
33	Operation	operator: 37 operands: 36
34	Operation	operator: 37 operands: 38
35	Literal
36	ExprTuple	39, 41
37	Literal
38	ExprTuple	40, 41
39	Operation	operator: 43 operand: 45
40	Operation	operator: 43 operand: 46
41	Literal
42	ExprTuple	45
43	Literal
44	ExprTuple	46
45	Variable
46	Variable