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, X
from proveit.linear_algebra import HilbertSpaces, Hspace, LinMap
from proveit.logic import Forall, InClass, InSet
from proveit.physics.quantum import Qmult, QmultCodomain, var_ket_psi

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [Hspace, X], instance_expr = Forall(instance_param_or_params = [A], instance_expr = Forall(instance_param_or_params = [var_ket_psi], instance_expr = InClass(Qmult(A, var_ket_psi), QmultCodomain), domain = Hspace), condition = InSet(Qmult(A), 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 \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces}}~\left[\forall_{A~|~\left[A\right] \in \mathcal{L}\left(\mathcal{H}, X\right)}~\left[\forall_{\lvert \psi \rangle \in \mathcal{H}}~\left(\left(A \thinspace \lvert \psi \rangle\right) \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}\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: 18 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 28 body: 3
3	Conditional	value: 4 condition: 5
4	Operation	operator: 18 operand: 9
5	Operation	operator: 7 operands: 8
6	ExprTuple	9
7	Literal
8	ExprTuple	10, 11
9	Lambda	parameter: 41 body: 12
10	Operation	operator: 32 operands: 13
11	Operation	operator: 32 operands: 14
12	Conditional	value: 15 condition: 16
13	ExprTuple	38, 17
14	ExprTuple	31, 17
15	Operation	operator: 18 operand: 21
16	Operation	operator: 34 operands: 20
17	Literal
18	Literal
19	ExprTuple	21
20	ExprTuple	22, 23
21	Lambda	parameter: 42 body: 25
22	Operation	operator: 39 operand: 41
23	Operation	operator: 27 operands: 28
24	ExprTuple	42
25	Conditional	value: 29 condition: 30
26	ExprTuple	41
27	Literal
28	ExprTuple	38, 31
29	Operation	operator: 32 operands: 33
30	Operation	operator: 34 operands: 35
31	Variable
32	Literal
33	ExprTuple	36, 37
34	Literal
35	ExprTuple	42, 38
36	Operation	operator: 39 operands: 40
37	Literal
38	Variable
39	Literal
40	ExprTuple	41, 42
41	Variable
42	Variable