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, U, n
from proveit.linear_algebra import Adj, Unitary
from proveit.logic import Equals, Exists
from proveit.numbers import sqrt
from proveit.physics.quantum import Qmult

# build up the expression from sub-expressions
expr = Exists(instance_param_or_params = [U], instance_expr = Equals(A, Qmult(U, sqrt(Qmult(Adj(A), A)))), domain = Unitary(n))

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_{U \in \textrm{U}\left(n\right)}~\left(A = \left(U \thinspace \sqrt{\left(A^{\dagger} \thinspace A\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	parameter: 17 body: 5
4	ExprTuple	17
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operands: 9
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	33, 12
10	Literal
11	ExprTuple	17, 13
12	Operation	operator: 24 operands: 14
13	Operation	operator: 15 operand: 19
14	ExprTuple	17, 18
15	Literal
16	ExprTuple	19
17	Variable
18	Operation	operator: 20 operands: 21
19	Variable
20	Literal
21	ExprTuple	22, 23
22	Operation	operator: 24 operands: 25
23	Operation	operator: 26 operands: 27
24	Literal
25	ExprTuple	28, 33
26	Literal
27	ExprTuple	29, 30
28	Operation	operator: 31 operand: 33
29	Literal
30	Literal
31	Literal
32	ExprTuple	33
33	Variable