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, alpha, x
from proveit.linear_algebra import ScalarMult
from proveit.logic import Forall, InSet
from proveit.numbers import Complex
from proveit.physics.quantum import QubitSpace

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [alpha], instance_expr = InSet(ScalarMult(alpha, x), QubitSpace), domain = Complex), 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_{\alpha \in \mathbb{C}}~\left(\left(\alpha \cdot 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	21, 15
6	Lambda	parameter: 20 body: 8
7	ExprTuple	20
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	20, 22
14	Operation	operator: 16 operands: 17
15	Operation	operator: 18 operands: 19
16	Literal
17	ExprTuple	20, 21
18	Literal
19	ExprTuple	22, 23
20	Variable
21	Variable
22	Literal
23	Literal