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 A, B, X, Y
from proveit.linear_algebra import HilbertSpaces, Hspace, LinMap
from proveit.logic import Forall, InSet
from proveit.physics.quantum import Qmult

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [Hspace, X, Y], instance_expr = Forall(instance_param_or_params = [A, B], instance_expr = InSet(Qmult(A, B), LinMap(Hspace, Y)), conditions = [InSet(Qmult(A), LinMap(X, Y)), InSet(Qmult(B), LinMap(Hspace, X))]), domain = 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())

\forall_{\mathcal{H}, X, Y \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces}}~\left[\forall_{A, B~|~\left[A\right] \in \mathcal{L}\left(X, Y\right), \left[B\right] \in \mathcal{L}\left(\mathcal{H}, X\right)}~\left(\left(A \thinspace B\right) \in \mathcal{L}\left(\mathcal{H}, Y\right)\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: 7 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 3 body: 4
3	ExprTuple	47, 48, 45
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 10
6	Operation	operator: 23 operands: 9
7	Literal
8	ExprTuple	10
9	ExprTuple	11, 12, 13
10	Lambda	parameters: 29 body: 14
11	Operation	operator: 17 operands: 15
12	Operation	operator: 17 operands: 16
13	Operation	operator: 17 operands: 18
14	Conditional	value: 19 condition: 20
15	ExprTuple	47, 21
16	ExprTuple	48, 21
17	Literal
18	ExprTuple	45, 21
19	Operation	operator: 32 operands: 22
20	Operation	operator: 23 operands: 24
21	Literal
22	ExprTuple	25, 26
23	Literal
24	ExprTuple	27, 28
25	Operation	operator: 40 operands: 29
26	Operation	operator: 42 operands: 30
27	Operation	operator: 32 operands: 31
28	Operation	operator: 32 operands: 33
29	ExprTuple	44, 46
30	ExprTuple	47, 45
31	ExprTuple	34, 35
32	Literal
33	ExprTuple	36, 37
34	Operation	operator: 40 operand: 44
35	Operation	operator: 42 operands: 39
36	Operation	operator: 40 operand: 46
37	Operation	operator: 42 operands: 43
38	ExprTuple	44
39	ExprTuple	48, 45
40	Literal
41	ExprTuple	46
42	Literal
43	ExprTuple	47, 48
44	Variable
45	Variable
46	Variable
47	Variable
48	Variable