Expression of type Exists

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 A, B, X, Y
from proveit.linear_algebra import HilbertSpaces, Hspace, LinMap
from proveit.logic import Exists, InSet, Set
from proveit.numbers import Complex
from proveit.physics.quantum import Qmult, QmultCodomain

# build up the expression from sub-expressions
sub_expr1 = LinMap(Hspace, X)
expr = Exists(instance_param_or_params = [Hspace, X, Y], instance_expr = InSet([Qmult(A), Qmult(B)], Set([sub_expr1, Hspace], [X, LinMap(Hspace, Complex)], [LinMap(X, Y), sub_expr1], [Complex, QmultCodomain], [QmultCodomain, Complex])), domain = 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())

\exists_{\mathcal{H}, X, Y \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces}}~\left(\left(\left[A\right], \left[B\right]\right) \in \left\{\left(\mathcal{L}\left(\mathcal{H}, X\right), \mathcal{H}\right), \left(X, \mathcal{L}\left(\mathcal{H}, \mathbb{C}\right)\right), \left(\mathcal{L}\left(X, Y\right), \mathcal{L}\left(\mathcal{H}, X\right)\right), \left(\mathbb{C}, \mathcal{Q^*}\right), \left(\mathcal{Q^*}, \mathbb{C}\right)\right\}\right)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

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