Expression of type ExprTuple

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 ExprTuple, n
from proveit.linear_algebra import OrthoNormBases
from proveit.logic import CartExp, InSet, Set
from proveit.numbers import Complex
from proveit.physics.quantum.algebra import v_1_to_n_kets, w_1_to_n_kets

# build up the expression from sub-expressions
sub_expr1 = OrthoNormBases(CartExp(Complex, n))
expr = ExprTuple(InSet(Set(v_1_to_n_kets), sub_expr1), InSet(Set(w_1_to_n_kets), sub_expr1))

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())

\left(\left\{\left\{\lvert v_{1} \rangle, \lvert v_{2} \rangle, \ldots, \lvert v_{n} \rangle\right\}\right\} \in \textrm{O.N.Bases}\left(\mathbb{C}^{n}\right), \left\{\left\{\lvert w_{1} \rangle, \lvert w_{2} \rangle, \ldots, \lvert w_{n} \rangle\right\}\right\} \in \textrm{O.N.Bases}\left(\mathbb{C}^{n}\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 4 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 8
4	Literal
5	ExprTuple	7, 8
6	Operation	operator: 17 operand: 13
7	Operation	operator: 17 operand: 14
8	Operation	operator: 11 operand: 15
9	ExprTuple	13
10	ExprTuple	14
11	Literal
12	ExprTuple	15
13	Operation	operator: 17 operands: 16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 19 operands: 20
16	ExprTuple	21
17	Literal
18	ExprTuple	22
19	Literal
20	ExprTuple	23, 27
21	ExprRange	lambda_map: 24 start_index: 26 end_index: 27
22	ExprRange	lambda_map: 25 start_index: 26 end_index: 27
23	Literal
24	Lambda	parameter: 38 body: 28
25	Lambda	parameter: 38 body: 29
26	Literal
27	Variable
28	Operation	operator: 31 operand: 33
29	Operation	operator: 31 operand: 34
30	ExprTuple	33
31	Literal
32	ExprTuple	34
33	IndexedVar	variable: 35 index: 38
34	IndexedVar	variable: 36 index: 38
35	Variable
36	Variable
37	ExprTuple	38
38	Variable