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, K, V, a, b
from proveit.linear_algebra import InnerProd, Norm, VecAdd, VecSpaces
from proveit.logic import Equals, Forall, InClass
from proveit.numbers import Add, Exp, sqrt, two, zero

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [a, b], instance_expr = Equals(Norm(VecAdd(a, b)), sqrt(Add(Exp(Norm(a), two), Exp(Norm(b), two)))), domain = V, condition = Equals(InnerProd(a, b), zero)), InClass(V, VecSpaces(K)))

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\{\forall_{a, b \in V~|~\left \langle a, b\right \rangle = 0}~\left(\left \|a + b\right \| = \sqrt{\left(\left \|a\right \|^{2} + \left \|b\right \|^{2}\right)}\right) \textrm{ if } V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)\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: 3 operand: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	33, 8
7	Lambda	parameters: 42 body: 9
8	Operation	operator: 10 operand: 14
9	Conditional	value: 12 condition: 13
10	Literal
11	ExprTuple	14
12	Operation	operator: 28 operands: 15
13	Operation	operator: 16 operands: 17
14	Variable
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	20, 21, 22
18	Operation	operator: 53 operand: 30
19	Operation	operator: 47 operands: 24
20	Operation	operator: 26 operands: 25
21	Operation	operator: 26 operands: 27
22	Operation	operator: 28 operands: 29
23	ExprTuple	30
24	ExprTuple	31, 32
25	ExprTuple	55, 33
26	Literal
27	ExprTuple	56, 33
28	Literal
29	ExprTuple	34, 35
30	Operation	operator: 36 operands: 42
31	Operation	operator: 37 operands: 38
32	Operation	operator: 39 operands: 40
33	Variable
34	Operation	operator: 41 operands: 42
35	Literal
36	Literal
37	Literal
38	ExprTuple	43, 44
39	Literal
40	ExprTuple	45, 51
41	Literal
42	ExprTuple	55, 56
43	Operation	operator: 47 operands: 46
44	Operation	operator: 47 operands: 48
45	Literal
46	ExprTuple	49, 51
47	Literal
48	ExprTuple	50, 51
49	Operation	operator: 53 operand: 55
50	Operation	operator: 53 operand: 56
51	Literal
52	ExprTuple	55
53	Literal
54	ExprTuple	56
55	Variable
56	Variable