Expression of type Lambda

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 Lambda, X, x
from proveit.linear_algebra import HilbertSpaces, Hspace, LinMap
from proveit.logic import Equals, Exists, InClass, InSet, Or
from proveit.physics.quantum import QmultCodomain

# build up the expression from sub-expressions
expr = Lambda(x, Equals(InClass(x, QmultCodomain), Or(Exists(instance_param_or_params = [Hspace], instance_expr = InSet(x, Hspace), domain = HilbertSpaces), Exists(instance_param_or_params = [Hspace, X], instance_expr = InSet(x, LinMap(Hspace, X)), domain = HilbertSpaces)).with_wrapping_at(2)))

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())

x \mapsto \left(\left(x \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}\right) = \left(\begin{array}{c} \left[\exists_{\mathcal{H} \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces}}~\left(x \in \mathcal{H}\right)\right] \lor  \\ \left[\exists_{\mathcal{H}, X \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces}}~\left(x \in \mathcal{L}\left(\mathcal{H}, X\right)\right)\right] \end{array}\right)\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 29 body: 2
1	ExprTuple	29
2	Operation	operator: 3 operands: 4
3	Literal
4	ExprTuple	5, 6
5	Operation	operator: 36 operands: 7
6	Operation	operator: 8 operands: 9
7	ExprTuple	29, 10
8	Literal
9	ExprTuple	11, 12
10	Literal
11	Operation	operator: 14 operand: 16
12	Operation	operator: 14 operand: 17
13	ExprTuple	16
14	Literal
15	ExprTuple	17
16	Lambda	parameter: 38 body: 19
17	Lambda	parameters: 34 body: 20
18	ExprTuple	38
19	Conditional	value: 21 condition: 31
20	Conditional	value: 22 condition: 23
21	Operation	operator: 25 operands: 24
22	Operation	operator: 25 operands: 26
23	Operation	operator: 27 operands: 28
24	ExprTuple	29, 38
25	Literal
26	ExprTuple	29, 30
27	Literal
28	ExprTuple	31, 32
29	Variable
30	Operation	operator: 33 operands: 34
31	Operation	operator: 36 operands: 35
32	Operation	operator: 36 operands: 37
33	Literal
34	ExprTuple	38, 39
35	ExprTuple	38, 40
36	Literal
37	ExprTuple	39, 40
38	Variable
39	Variable
40	Literal