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, alpha, n
from proveit.linear_algebra import Norm
from proveit.logic import CartExp, Equals, Forall, InSet
from proveit.numbers import Complex, RealNonNeg
from proveit.physics.quantum import Qmult, var_ket_psi

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

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 \|\lvert \psi \rangle\right \| = \alpha}~\left(\left \|U \thinspace \lvert \psi \rangle\right \| = \alpha\right) \textrm{ if } \alpha \in \mathbb{R}^{\ge 0}\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: 18 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	25, 7
6	Lambda	parameter: 35 body: 8
7	Literal
8	Conditional	value: 9 condition: 10
9	Operation	operator: 20 operands: 11
10	Operation	operator: 12 operands: 13
11	ExprTuple	14, 25
12	Literal
13	ExprTuple	15, 16
14	Operation	operator: 30 operand: 22
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operands: 21
17	ExprTuple	22
18	Literal
19	ExprTuple	35, 23
20	Literal
21	ExprTuple	24, 25
22	Operation	operator: 26 operands: 27
23	Operation	operator: 28 operands: 29
24	Operation	operator: 30 operand: 35
25	Variable
26	Literal
27	ExprTuple	32, 35
28	Literal
29	ExprTuple	33, 34
30	Literal
31	ExprTuple	35
32	Variable
33	Literal
34	Variable
35	Variable