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

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(K, Forall(instance_param_or_params = [V], instance_expr = 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)), domain = 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(K \mapsto \left[\forall_{V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\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)\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: 20 body: 2
2	Operation	operator: 9 operand: 4
3	ExprTuple	4
4	Lambda	parameter: 39 body: 6
5	ExprTuple	39
6	Conditional	value: 7 condition: 8
7	Operation	operator: 9 operand: 13
8	Operation	operator: 11 operands: 12
9	Literal
10	ExprTuple	13
11	Literal
12	ExprTuple	39, 14
13	Lambda	parameters: 48 body: 15
14	Operation	operator: 16 operand: 20
15	Conditional	value: 18 condition: 19
16	Literal
17	ExprTuple	20
18	Operation	operator: 34 operands: 21
19	Operation	operator: 22 operands: 23
20	Variable
21	ExprTuple	24, 25
22	Literal
23	ExprTuple	26, 27, 28
24	Operation	operator: 59 operand: 36
25	Operation	operator: 53 operands: 30
26	Operation	operator: 32 operands: 31
27	Operation	operator: 32 operands: 33
28	Operation	operator: 34 operands: 35
29	ExprTuple	36
30	ExprTuple	37, 38
31	ExprTuple	61, 39
32	Literal
33	ExprTuple	62, 39
34	Literal
35	ExprTuple	40, 41
36	Operation	operator: 42 operands: 48
37	Operation	operator: 43 operands: 44
38	Operation	operator: 45 operands: 46
39	Variable
40	Operation	operator: 47 operands: 48
41	Literal
42	Literal
43	Literal
44	ExprTuple	49, 50
45	Literal
46	ExprTuple	51, 57
47	Literal
48	ExprTuple	61, 62
49	Operation	operator: 53 operands: 52
50	Operation	operator: 53 operands: 54
51	Literal
52	ExprTuple	55, 57
53	Literal
54	ExprTuple	56, 57
55	Operation	operator: 59 operand: 61
56	Operation	operator: 59 operand: 62
57	Literal
58	ExprTuple	61
59	Literal
60	ExprTuple	62
61	Variable
62	Variable