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.physics.quantum import Qmult

# build up the expression from sub-expressions
sub_expr1 = LinMap(Hspace, X)
expr = Forall(instance_param_or_params = [Hspace, X], instance_expr = Forall(instance_param_or_params = [A], instance_expr = InSet(Qmult(A, c), sub_expr1), condition = InSet(Qmult(A), sub_expr1)), 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(\left(A \thinspace c\right) \in \mathcal{L}\left(\mathcal{H}, X\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: 6 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 30 body: 3
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 10
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	11, 12
10	Lambda	parameter: 32 body: 13
11	Operation	operator: 15 operands: 14
12	Operation	operator: 15 operands: 16
13	Conditional	value: 17 condition: 18
14	ExprTuple	33, 19
15	Literal
16	ExprTuple	34, 19
17	Operation	operator: 21 operands: 20
18	Operation	operator: 21 operands: 22
19	Literal
20	ExprTuple	23, 25
21	Literal
22	ExprTuple	24, 25
23	Operation	operator: 27 operands: 26
24	Operation	operator: 27 operand: 32
25	Operation	operator: 29 operands: 30
26	ExprTuple	32, 31
27	Literal
28	ExprTuple	32
29	Literal
30	ExprTuple	33, 34
31	Variable
32	Variable
33	Variable
34	Variable