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

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