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 A, Conditional, X, c
from proveit.linear_algebra import HilbertSpaces, Hspace, LinMap
from proveit.logic import Forall, InSet
from proveit.numbers import Complex
from proveit.physics.quantum import Qmult

# build up the expression from sub-expressions
sub_expr1 = LinMap(Hspace, X)
expr = Conditional(Forall(instance_param_or_params = [Hspace, X], instance_expr = Forall(instance_param_or_params = [A], instance_expr = InSet(Qmult(c, A), sub_expr1), condition = InSet(Qmult(A), sub_expr1)), domain = HilbertSpaces), InSet(c, Complex))

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_{\mathcal{H}, X \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces}}~\left[\forall_{A~|~\left[A\right] \in \mathcal{L}\left(\mathcal{H}, X\right)}~\left(\left(c \thinspace A\right) \in \mathcal{L}\left(\mathcal{H}, X\right)\right)\right] \textrm{ if } c \in \mathbb{C}\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: 10 operand: 5
2	Operation	operator: 25 operands: 4
3	ExprTuple	5
4	ExprTuple	35, 6
5	Lambda	parameters: 34 body: 7
6	Literal
7	Conditional	value: 8 condition: 9
8	Operation	operator: 10 operand: 14
9	Operation	operator: 12 operands: 13
10	Literal
11	ExprTuple	14
12	Literal
13	ExprTuple	15, 16
14	Lambda	parameter: 36 body: 17
15	Operation	operator: 19 operands: 18
16	Operation	operator: 19 operands: 20
17	Conditional	value: 21 condition: 22
18	ExprTuple	37, 23
19	Literal
20	ExprTuple	38, 23
21	Operation	operator: 25 operands: 24
22	Operation	operator: 25 operands: 26
23	Literal
24	ExprTuple	27, 29
25	Literal
26	ExprTuple	28, 29
27	Operation	operator: 31 operands: 30
28	Operation	operator: 31 operand: 36
29	Operation	operator: 33 operands: 34
30	ExprTuple	35, 36
31	Literal
32	ExprTuple	36
33	Literal
34	ExprTuple	37, 38
35	Variable
36	Variable
37	Variable
38	Variable