Expression of type Lambda

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, 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 = 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(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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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