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, K, Lambda, 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 = ExprTuple(Lambda(V, 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(V \mapsto \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..\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	parameter: 36 body: 3
2	ExprTuple	36
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 10
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	36, 11
10	Lambda	parameters: 45 body: 12
11	Operation	operator: 13 operand: 17
12	Conditional	value: 15 condition: 16
13	Literal
14	ExprTuple	17
15	Operation	operator: 31 operands: 18
16	Operation	operator: 19 operands: 20
17	Variable
18	ExprTuple	21, 22
19	Literal
20	ExprTuple	23, 24, 25
21	Operation	operator: 56 operand: 33
22	Operation	operator: 50 operands: 27
23	Operation	operator: 29 operands: 28
24	Operation	operator: 29 operands: 30
25	Operation	operator: 31 operands: 32
26	ExprTuple	33
27	ExprTuple	34, 35
28	ExprTuple	58, 36
29	Literal
30	ExprTuple	59, 36
31	Literal
32	ExprTuple	37, 38
33	Operation	operator: 39 operands: 45
34	Operation	operator: 40 operands: 41
35	Operation	operator: 42 operands: 43
36	Variable
37	Operation	operator: 44 operands: 45
38	Literal
39	Literal
40	Literal
41	ExprTuple	46, 47
42	Literal
43	ExprTuple	48, 54
44	Literal
45	ExprTuple	58, 59
46	Operation	operator: 50 operands: 49
47	Operation	operator: 50 operands: 51
48	Literal
49	ExprTuple	52, 54
50	Literal
51	ExprTuple	53, 54
52	Operation	operator: 56 operand: 58
53	Operation	operator: 56 operand: 59
54	Literal
55	ExprTuple	58
56	Literal
57	ExprTuple	59
58	Variable
59	Variable