Expression of type Equals

from the theory of proveit.physics.quantum.algebra

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 X, x
from proveit.linear_algebra import HilbertSpaces, Hspace, LinMap
from proveit.logic import Equals, Exists, InClass, InSet, Or
from proveit.physics.quantum import QmultCodomain

# build up the expression from sub-expressions
expr = Equals(InClass(x, QmultCodomain), Or(Exists(instance_param_or_params = [Hspace], instance_expr = InSet(x, Hspace), domain = HilbertSpaces), Exists(instance_param_or_params = [Hspace, X], instance_expr = InSet(x, LinMap(Hspace, X)), domain = HilbertSpaces)).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(x \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}\right) = \left(\begin{array}{c} \left[\exists_{\mathcal{H} \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces}}~\left(x \in \mathcal{H}\right)\right] \lor  \\ \left[\exists_{\mathcal{H}, X \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces}}~\left(x \in \mathcal{L}\left(\mathcal{H}, X\right)\right)\right] \end{array}\right)

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

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