Expression of type Conditional

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 Conditional, U, n
from proveit.linear_algebra import Unitary
from proveit.logic import CartExp, Forall, InSet
from proveit.numbers import Complex
from proveit.physics.quantum import Qmult, var_ket_psi

# build up the expression from sub-expressions
sub_expr1 = CartExp(Complex, n)
expr = Conditional(Forall(instance_param_or_params = [var_ket_psi], instance_expr = InSet(Qmult(U, var_ket_psi), sub_expr1), domain = sub_expr1), InSet(U, 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())

\left\{\forall_{\lvert \psi \rangle \in \mathbb{C}^{n}}~\left(\left(U \thinspace \lvert \psi \rangle\right) \in \mathbb{C}^{n}\right) \textrm{ if } U \in \textrm{U}\left(n\right)\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operand: 6
2	Operation	operator: 15 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	23, 7
6	Lambda	parameter: 24 body: 9
7	Operation	operator: 10 operand: 26
8	ExprTuple	24
9	Conditional	value: 12 condition: 13
10	Literal
11	ExprTuple	26
12	Operation	operator: 15 operands: 14
13	Operation	operator: 15 operands: 16
14	ExprTuple	17, 18
15	Literal
16	ExprTuple	24, 18
17	Operation	operator: 19 operands: 20
18	Operation	operator: 21 operands: 22
19	Literal
20	ExprTuple	23, 24
21	Literal
22	ExprTuple	25, 26
23	Variable
24	Variable
25	Literal
26	Variable