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 Hspace, InnerProd, LinMap, OrthoProj, VecZero
from proveit.logic import And, Equals, Forall, Iff, Implies, InSet
from proveit.numbers import zero

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = ExprTuple(Lambda(P, Conditional(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), InSet(P, LinMap(Hspace, 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(P \mapsto \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} \textrm{ if } P \in \mathcal{L}\left(\mathcal{H}, \mathcal{H}\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: 46 body: 3
2	ExprTuple	46
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 55 operands: 8
6	Literal
7	ExprTuple	9, 10
8	ExprTuple	46, 11
9	Operation	operator: 53 operands: 12
10	Operation	operator: 13 operands: 14
11	Operation	operator: 15 operands: 16
12	ExprTuple	46, 17
13	Literal
14	ExprTuple	18, 19
15	Literal
16	ExprTuple	52, 52
17	Operation	operator: 20 operands: 21
18	Operation	operator: 38 operand: 24
19	Operation	operator: 38 operand: 25
20	Literal
21	ExprTuple	52, 59
22	ExprTuple	24
23	ExprTuple	25
24	Lambda	parameter: 62 body: 26
25	Lambda	parameter: 63 body: 27
26	Conditional	value: 28 condition: 51
27	Conditional	value: 29 condition: 30
28	Operation	operator: 53 operands: 31
29	Operation	operator: 32 operands: 33
30	Operation	operator: 55 operands: 34
31	ExprTuple	35, 62
32	Literal
33	ExprTuple	36, 37
34	ExprTuple	63, 52
35	Operation	operator: 46 operand: 62
36	Operation	operator: 38 operand: 41
37	Operation	operator: 53 operands: 40
38	Literal
39	ExprTuple	41
40	ExprTuple	42, 43
41	Lambda	parameter: 62 body: 45
42	Operation	operator: 46 operand: 63
43	Operation	operator: 48 operand: 52
44	ExprTuple	62
45	Conditional	value: 50 condition: 51
46	Variable
47	ExprTuple	63
48	Literal
49	ExprTuple	52
50	Operation	operator: 53 operands: 54
51	Operation	operator: 55 operands: 56
52	Variable
53	Literal
54	ExprTuple	57, 58
55	Literal
56	ExprTuple	62, 59
57	Operation	operator: 60 operands: 61
58	Literal
59	Variable
60	Literal
61	ExprTuple	62, 63
62	Variable
63	Variable