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, NaturalPos
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 = [U], instance_expr = Forall(instance_param_or_params = [var_ket_psi], instance_expr = InSet(Qmult(U, var_ket_psi), sub_expr1), domain = sub_expr1), domain = Unitary(n)), InSet(n, NaturalPos))

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(n\right)}~\left[\forall_{\lvert \psi \rangle \in \mathbb{C}^{n}}~\left(\left(U \thinspace \lvert \psi \rangle\right) \in \mathbb{C}^{n}\right)\right] \textrm{ if } n \in \mathbb{N}^+\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: 11 operand: 5
2	Operation	operator: 23 operands: 4
3	ExprTuple	5
4	ExprTuple	34, 6
5	Lambda	parameter: 31 body: 8
6	Literal
7	ExprTuple	31
8	Conditional	value: 9 condition: 10
9	Operation	operator: 11 operand: 14
10	Operation	operator: 23 operands: 13
11	Literal
12	ExprTuple	14
13	ExprTuple	31, 15
14	Lambda	parameter: 32 body: 17
15	Operation	operator: 18 operand: 34
16	ExprTuple	32
17	Conditional	value: 20 condition: 21
18	Literal
19	ExprTuple	34
20	Operation	operator: 23 operands: 22
21	Operation	operator: 23 operands: 24
22	ExprTuple	25, 26
23	Literal
24	ExprTuple	32, 26
25	Operation	operator: 27 operands: 28
26	Operation	operator: 29 operands: 30
27	Literal
28	ExprTuple	31, 32
29	Literal
30	ExprTuple	33, 34
31	Variable
32	Variable
33	Literal
34	Variable