Expression of type Conditional

from the theory of proveit.physics.quantum

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, x
from proveit.linear_algebra import Unitary
from proveit.logic import Forall, InSet
from proveit.numbers import two
from proveit.physics.quantum import Qmult, QubitSpace

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [U], instance_expr = InSet(Qmult(U, x), QubitSpace), domain = Unitary(two)), InSet(x, QubitSpace))

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_{U \in \textrm{U}\left(2\right)}~\left(\left(U \thinspace x\right) \in \mathbb{C}^{2}\right) \textrm{ if } x \in \mathbb{C}^{2}\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: 12 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	24, 15
6	Lambda	parameter: 23 body: 8
7	ExprTuple	23
8	Conditional	value: 9 condition: 10
9	Operation	operator: 12 operands: 11
10	Operation	operator: 12 operands: 13
11	ExprTuple	14, 15
12	Literal
13	ExprTuple	23, 16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 19 operands: 20
16	Operation	operator: 21 operand: 26
17	Literal
18	ExprTuple	23, 24
19	Literal
20	ExprTuple	25, 26
21	Literal
22	ExprTuple	26
23	Variable
24	Variable
25	Literal
26	Literal