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, X
from proveit.linear_algebra import HilbertSpaces, Hspace, OrthoProj
from proveit.logic import Equals, Forall, InClass, SubsetEq
from proveit.numbers import Exp, two

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(Hspace, Conditional(Forall(instance_param_or_params = [X], instance_expr = Forall(instance_param_or_params = [P], instance_expr = Equals(Exp(P, two), P), condition = Equals(P, OrthoProj(Hspace, X))), condition = SubsetEq(X, Hspace)), InClass(Hspace, HilbertSpaces))))

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(\mathcal{H} \mapsto \left\{\forall_{X~|~X \subseteq \mathcal{H}}~\left[\forall_{P~|~P = \textrm{OrthoProj}\left(\mathcal{H}, X\right)}~\left(P^{2} = P\right)\right] \textrm{ if } \mathcal{H} \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces}\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: 35 body: 3
2	ExprTuple	35
3	Conditional	value: 4 condition: 5
4	Operation	operator: 15 operand: 9
5	Operation	operator: 7 operands: 8
6	ExprTuple	9
7	Literal
8	ExprTuple	35, 10
9	Lambda	parameter: 36 body: 12
10	Literal
11	ExprTuple	36
12	Conditional	value: 13 condition: 14
13	Operation	operator: 15 operand: 19
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprTuple	19
17	Literal
18	ExprTuple	36, 35
19	Lambda	parameter: 33 body: 21
20	ExprTuple	33
21	Conditional	value: 22 condition: 23
22	Operation	operator: 25 operands: 24
23	Operation	operator: 25 operands: 26
24	ExprTuple	27, 33
25	Literal
26	ExprTuple	33, 28
27	Operation	operator: 29 operands: 30
28	Operation	operator: 31 operands: 32
29	Literal
30	ExprTuple	33, 34
31	Literal
32	ExprTuple	35, 36
33	Variable
34	Literal
35	Variable
36	Variable