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 X
from proveit.linear_algebra import Hspace
from proveit.logic import Forall, InClass, InSet
from proveit.physics.quantum import Qmult, QmultCodomain, bra_varphi, ket_varphi, var_ket_psi, varphi

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [Hspace, X], instance_expr = Forall(instance_param_or_params = [var_ket_psi], instance_expr = Forall(instance_param_or_params = [varphi], instance_expr = InClass(Qmult(var_ket_psi, bra_varphi), QmultCodomain), condition = InSet(ket_varphi, X)), domain = Hspace))

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}~\left[\forall_{\lvert \psi \rangle \in \mathcal{H}}~\left[\forall_{\varphi~|~\lvert \varphi \rangle \in X}~\left(\left(\lvert \psi \rangle \thinspace \langle \varphi \rvert\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: 11 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 3 body: 4
3	ExprTuple	15, 26
4	Operation	operator: 11 operand: 6
5	ExprTuple	6
6	Lambda	parameter: 30 body: 8
7	ExprTuple	30
8	Conditional	value: 9 condition: 10
9	Operation	operator: 11 operand: 14
10	Operation	operator: 21 operands: 13
11	Literal
12	ExprTuple	14
13	ExprTuple	30, 15
14	Lambda	parameter: 34 body: 16
15	Variable
16	Conditional	value: 17 condition: 18
17	Operation	operator: 19 operands: 20
18	Operation	operator: 21 operands: 22
19	Literal
20	ExprTuple	23, 24
21	Literal
22	ExprTuple	25, 26
23	Operation	operator: 27 operands: 28
24	Literal
25	Operation	operator: 29 operand: 34
26	Variable
27	Literal
28	ExprTuple	30, 31
29	Literal
30	Variable
31	Operation	operator: 32 operand: 34
32	Literal
33	ExprTuple	34
34	Variable