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, c
from proveit.linear_algebra import HilbertSpaces, Hspace, LinMap
from proveit.logic import Forall, InSet
from proveit.numbers import Complex
from proveit.physics.quantum import Qmult

# build up the expression from sub-expressions
sub_expr1 = LinMap(Hspace, X)
expr = Forall(instance_param_or_params = [c], instance_expr = Forall(instance_param_or_params = [Hspace, X], instance_expr = Forall(instance_param_or_params = [A], instance_expr = InSet(Qmult(c, A), sub_expr1), condition = InSet(Qmult(A), sub_expr1)), domain = HilbertSpaces), domain = Complex)

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_{c \in \mathbb{C}}~\left[\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(\left(c \thinspace A\right) \in \mathcal{L}\left(\mathcal{H}, X\right)\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: 14 operand: 2
1	ExprTuple	2
2	Lambda	parameter: 39 body: 4
3	ExprTuple	39
4	Conditional	value: 5 condition: 6
5	Operation	operator: 14 operand: 9
6	Operation	operator: 29 operands: 8
7	ExprTuple	9
8	ExprTuple	39, 10
9	Lambda	parameters: 38 body: 11
10	Literal
11	Conditional	value: 12 condition: 13
12	Operation	operator: 14 operand: 18
13	Operation	operator: 16 operands: 17
14	Literal
15	ExprTuple	18
16	Literal
17	ExprTuple	19, 20
18	Lambda	parameter: 40 body: 21
19	Operation	operator: 23 operands: 22
20	Operation	operator: 23 operands: 24
21	Conditional	value: 25 condition: 26
22	ExprTuple	41, 27
23	Literal
24	ExprTuple	42, 27
25	Operation	operator: 29 operands: 28
26	Operation	operator: 29 operands: 30
27	Literal
28	ExprTuple	31, 33
29	Literal
30	ExprTuple	32, 33
31	Operation	operator: 35 operands: 34
32	Operation	operator: 35 operand: 40
33	Operation	operator: 37 operands: 38
34	ExprTuple	39, 40
35	Literal
36	ExprTuple	40
37	Literal
38	ExprTuple	41, 42
39	Variable
40	Variable
41	Variable
42	Variable