Expression of type Forall

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

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [x], instance_expr = 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())

\forall_{x}~\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()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameter: 32 body: 5
4	ExprTuple	32
5	Operation	operator: 6 operands: 7
6	Literal
7	ExprTuple	8, 9
8	Operation	operator: 39 operands: 10
9	Operation	operator: 11 operands: 12
10	ExprTuple	32, 13
11	Literal
12	ExprTuple	14, 15
13	Literal
14	Operation	operator: 17 operand: 19
15	Operation	operator: 17 operand: 20
16	ExprTuple	19
17	Literal
18	ExprTuple	20
19	Lambda	parameter: 41 body: 22
20	Lambda	parameters: 37 body: 23
21	ExprTuple	41
22	Conditional	value: 24 condition: 34
23	Conditional	value: 25 condition: 26
24	Operation	operator: 28 operands: 27
25	Operation	operator: 28 operands: 29
26	Operation	operator: 30 operands: 31
27	ExprTuple	32, 41
28	Literal
29	ExprTuple	32, 33
30	Literal
31	ExprTuple	34, 35
32	Variable
33	Operation	operator: 36 operands: 37
34	Operation	operator: 39 operands: 38
35	Operation	operator: 39 operands: 40
36	Literal
37	ExprTuple	41, 42
38	ExprTuple	41, 43
39	Literal
40	ExprTuple	42, 43
41	Variable
42	Variable
43	Literal