Theorem qmult_ket_ket_is_ket of type Forall

from the theory of proveit.physics.quantum.algebra

see dependencies

import proveit
# Automation is not needed when only building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_theorem_expr # Load the stored theorem expression as 'stored_expr'
# import the special expression
from proveit.physics.quantum.algebra import qmult_ket_ket_is_ket

# check that the built expression is the same as the stored expression
assert qmult_ket_ket_is_ket.expr == stored_expr
assert qmult_ket_ket_is_ket.expr._style_id == stored_expr._style_id
print("Passed sanity check: qmult_ket_ket_is_ket matches stored_expr")

Passed sanity check: qmult_ket_ket_is_ket matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\forall_{A, B \underset{{\scriptscriptstyle c}}{\in} \textrm{HilbertSpaces}}~\left[\forall_{\lvert \psi \rangle \in A, \lvert \varphi \rangle \in B}~\left(\left(\lvert \psi \rangle \thinspace \lvert \varphi \rangle\right) \in \left(A {\otimes} B\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: 29 body: 3
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 20 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	10, 11
9	Lambda	parameters: 27 body: 12
10	Operation	operator: 14 operands: 13
11	Operation	operator: 14 operands: 15
12	Conditional	value: 16 condition: 17
13	ExprTuple	34, 18
14	Literal
15	ExprTuple	36, 18
16	Operation	operator: 31 operands: 19
17	Operation	operator: 20 operands: 21
18	Literal
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	24, 25
22	Operation	operator: 26 operands: 27
23	Operation	operator: 28 operands: 29
24	Operation	operator: 31 operands: 30
25	Operation	operator: 31 operands: 32
26	Literal
27	ExprTuple	33, 35
28	Literal
29	ExprTuple	34, 36
30	ExprTuple	33, 34
31	Literal
32	ExprTuple	35, 36
33	Variable
34	Variable
35	Variable
36	Variable