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 And, Forall, InClass, InSet
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 = [A], instance_expr = InSet(Qmult(c, A), sub_expr1), condition = InSet(Qmult(A), sub_expr1)), And(InClass(Hspace, HilbertSpaces), InClass(X, HilbertSpaces)))

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_{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) \textrm{ if } \mathcal{H} \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces} ,  X \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces}\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: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	8, 9
7	Lambda	parameter: 29 body: 10
8	Operation	operator: 12 operands: 11
9	Operation	operator: 12 operands: 13
10	Conditional	value: 14 condition: 15
11	ExprTuple	30, 16
12	Literal
13	ExprTuple	31, 16
14	Operation	operator: 18 operands: 17
15	Operation	operator: 18 operands: 19
16	Literal
17	ExprTuple	20, 22
18	Literal
19	ExprTuple	21, 22
20	Operation	operator: 24 operands: 23
21	Operation	operator: 24 operand: 29
22	Operation	operator: 26 operands: 27
23	ExprTuple	28, 29
24	Literal
25	ExprTuple	29
26	Literal
27	ExprTuple	30, 31
28	Variable
29	Variable
30	Variable
31	Variable