Expression of type Or

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 Exists, InSet, Or

# build up the expression from sub-expressions
expr = 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())

\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}

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.	()	(2)	('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',)

# 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: 6 operand: 8
4	Operation	operator: 6 operand: 9
5	ExprTuple	8
6	Literal
7	ExprTuple	9
8	Lambda	parameter: 30 body: 11
9	Lambda	parameters: 26 body: 12
10	ExprTuple	30
11	Conditional	value: 13 condition: 23
12	Conditional	value: 14 condition: 15
13	Operation	operator: 17 operands: 16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 19 operands: 20
16	ExprTuple	21, 30
17	Literal
18	ExprTuple	21, 22
19	Literal
20	ExprTuple	23, 24
21	Variable
22	Operation	operator: 25 operands: 26
23	Operation	operator: 28 operands: 27
24	Operation	operator: 28 operands: 29
25	Literal
26	ExprTuple	30, 31
27	ExprTuple	30, 32
28	Literal
29	ExprTuple	31, 32
30	Variable
31	Variable
32	Literal