Expression of type ExprTuple

from the theory of proveit.linear_algebra.inner_products

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, P, Px, Py, X, x, y
from proveit.linear_algebra import HilbertSpaces, Hspace, InnerProd, LinMap, OrthoProj, VecZero
from proveit.logic import And, Equals, Forall, Iff, Implies, InClass, SubsetEq
from proveit.numbers import zero

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = ExprTuple(Lambda([Hspace, X], Conditional(Forall(instance_param_or_params = [P], instance_expr = Iff(Equals(P, OrthoProj(Hspace, X)), And(Forall(instance_param_or_params = sub_expr1, instance_expr = Equals(Px, x), domain = X), Forall(instance_param_or_params = [y], instance_expr = Implies(Forall(instance_param_or_params = sub_expr1, instance_expr = Equals(InnerProd(x, y), zero), domain = X), Equals(Py, VecZero(Hspace))), domain = Hspace)).with_wrapping_at(2)).with_wrapping_at(2), domain = LinMap(Hspace, Hspace)), And(InClass(Hspace, HilbertSpaces), InClass(X, HilbertSpaces), SubsetEq(X, Hspace)))))

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(\mathcal{H}, X\right) \mapsto \left\{\forall_{P \in \mathcal{L}\left(\mathcal{H}, \mathcal{H}\right)}~\left(\begin{array}{c} \begin{array}{l} \left(P = \textrm{OrthoProj}\left(\mathcal{H}, X\right)\right) \Leftrightarrow  \\ \left(\begin{array}{c} \left[\forall_{x \in X}~\left(P\left(x\right) = x\right)\right] \land  \\ \left[\forall_{y \in \mathcal{H}}~\left(\left[\forall_{x \in X}~\left(\left \langle x, y\right \rangle = 0\right)\right] \Rightarrow \left(P\left(y\right) = \vec{0}\left(\mathcal{H}\right)\right)\right)\right] \end{array}\right) \end{array} \end{array}\right) \textrm{ if } \mathcal{H} \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces} ,  X \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces} ,  X \subseteq \mathcal{H}\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: 36 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 53 operand: 7
4	Operation	operator: 28 operands: 6
5	ExprTuple	7
6	ExprTuple	8, 9, 10
7	Lambda	parameter: 61 body: 12
8	Operation	operator: 14 operands: 13
9	Operation	operator: 14 operands: 15
10	Operation	operator: 16 operands: 17
11	ExprTuple	61
12	Conditional	value: 18 condition: 19
13	ExprTuple	67, 20
14	Literal
15	ExprTuple	74, 20
16	Literal
17	ExprTuple	74, 67
18	Operation	operator: 21 operands: 22
19	Operation	operator: 70 operands: 23
20	Literal
21	Literal
22	ExprTuple	24, 25
23	ExprTuple	61, 26
24	Operation	operator: 68 operands: 27
25	Operation	operator: 28 operands: 29
26	Operation	operator: 30 operands: 31
27	ExprTuple	61, 32
28	Literal
29	ExprTuple	33, 34
30	Literal
31	ExprTuple	67, 67
32	Operation	operator: 35 operands: 36
33	Operation	operator: 53 operand: 39
34	Operation	operator: 53 operand: 40
35	Literal
36	ExprTuple	67, 74
37	ExprTuple	39
38	ExprTuple	40
39	Lambda	parameter: 77 body: 41
40	Lambda	parameter: 78 body: 42
41	Conditional	value: 43 condition: 66
42	Conditional	value: 44 condition: 45
43	Operation	operator: 68 operands: 46
44	Operation	operator: 47 operands: 48
45	Operation	operator: 70 operands: 49
46	ExprTuple	50, 77
47	Literal
48	ExprTuple	51, 52
49	ExprTuple	78, 67
50	Operation	operator: 61 operand: 77
51	Operation	operator: 53 operand: 56
52	Operation	operator: 68 operands: 55
53	Literal
54	ExprTuple	56
55	ExprTuple	57, 58
56	Lambda	parameter: 77 body: 60
57	Operation	operator: 61 operand: 78
58	Operation	operator: 63 operand: 67
59	ExprTuple	77
60	Conditional	value: 65 condition: 66
61	Variable
62	ExprTuple	78
63	Literal
64	ExprTuple	67
65	Operation	operator: 68 operands: 69
66	Operation	operator: 70 operands: 71
67	Variable
68	Literal
69	ExprTuple	72, 73
70	Literal
71	ExprTuple	77, 74
72	Operation	operator: 75 operands: 76
73	Literal
74	Variable
75	Literal
76	ExprTuple	77, 78
77	Variable
78	Variable