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 ExprTuple, P, Px, Py, X, x, y
from proveit.linear_algebra import Hspace, InnerProd, OrthoProj, VecZero
from proveit.logic import And, Equals, Forall, Implies
from proveit.numbers import zero

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = ExprTuple(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))

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 = \textrm{OrthoProj}\left(\mathcal{H}, X\right), \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)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 42 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	35, 6
4	Literal
5	ExprTuple	7, 8
6	Operation	operator: 9 operands: 10
7	Operation	operator: 27 operand: 13
8	Operation	operator: 27 operand: 14
9	Literal
10	ExprTuple	41, 48
11	ExprTuple	13
12	ExprTuple	14
13	Lambda	parameter: 51 body: 15
14	Lambda	parameter: 52 body: 16
15	Conditional	value: 17 condition: 40
16	Conditional	value: 18 condition: 19
17	Operation	operator: 42 operands: 20
18	Operation	operator: 21 operands: 22
19	Operation	operator: 44 operands: 23
20	ExprTuple	24, 51
21	Literal
22	ExprTuple	25, 26
23	ExprTuple	52, 41
24	Operation	operator: 35 operand: 51
25	Operation	operator: 27 operand: 30
26	Operation	operator: 42 operands: 29
27	Literal
28	ExprTuple	30
29	ExprTuple	31, 32
30	Lambda	parameter: 51 body: 34
31	Operation	operator: 35 operand: 52
32	Operation	operator: 37 operand: 41
33	ExprTuple	51
34	Conditional	value: 39 condition: 40
35	Variable
36	ExprTuple	52
37	Literal
38	ExprTuple	41
39	Operation	operator: 42 operands: 43
40	Operation	operator: 44 operands: 45
41	Variable
42	Literal
43	ExprTuple	46, 47
44	Literal
45	ExprTuple	51, 48
46	Operation	operator: 49 operands: 50
47	Literal
48	Variable
49	Literal
50	ExprTuple	51, 52
51	Variable
52	Variable