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 Conditional, ExprTuple, Lambda, j, l, n
from proveit.core_expr_types import A_1_to_l, C_1_to_n, b_1_to_j
from proveit.logic import And, Equals, Forall, InClass, InSet
from proveit.numbers import Complex, Natural
from proveit.physics.quantum import Qmult, QmultCodomain

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([j, l, n], Conditional(Forall(instance_param_or_params = [b_1_to_j], instance_expr = Forall(instance_param_or_params = [A_1_to_l, C_1_to_n], instance_expr = Equals(Qmult(A_1_to_l, b_1_to_j, C_1_to_n), Qmult(b_1_to_j, A_1_to_l, C_1_to_n)).with_wrapping_at(2), condition = InClass(Qmult(A_1_to_l, C_1_to_n), QmultCodomain)), domain = Complex), And(InSet(j, Natural), InSet(l, Natural), InSet(n, Natural)))))

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(j, l, n\right) \mapsto \left\{\forall_{b_{1}, b_{2}, \ldots, b_{j} \in \mathbb{C}}~\left[\forall_{A_{1}, A_{2}, \ldots, A_{l}, C_{1}, C_{2}, \ldots, C_{n}~|~\left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{l}\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\right) \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}}~\left(\begin{array}{c} \begin{array}{l} \left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{l}\thinspace b_{1} \thinspace  b_{2} \thinspace  \ldots \thinspace  b_{j}\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\right) =  \\ \left(b_{1} \thinspace  b_{2} \thinspace  \ldots \thinspace  b_{j}\thinspace A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{l}\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\right) \end{array} \end{array}\right)\right] \textrm{ if } j \in \mathbb{N} ,  l \in \mathbb{N} ,  n \in \mathbb{N}\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 2 body: 3
2	ExprTuple	50, 52, 55
3	Conditional	value: 4 condition: 5
4	Operation	operator: 20 operand: 8
5	Operation	operator: 22 operands: 7
6	ExprTuple	8
7	ExprTuple	9, 10, 11
8	Lambda	parameters: 12 body: 13
9	Operation	operator: 35 operands: 14
10	Operation	operator: 35 operands: 15
11	Operation	operator: 35 operands: 16
12	ExprTuple	46
13	Conditional	value: 17 condition: 18
14	ExprTuple	50, 19
15	ExprTuple	52, 19
16	ExprTuple	55, 19
17	Operation	operator: 20 operand: 24
18	Operation	operator: 22 operands: 23
19	Literal
20	Literal
21	ExprTuple	24
22	Literal
23	ExprTuple	25
24	Lambda	parameters: 45 body: 26
25	ExprRange	lambda_map: 27 start_index: 54 end_index: 50
26	Conditional	value: 28 condition: 29
27	Lambda	parameter: 63 body: 30
28	Operation	operator: 31 operands: 32
29	Operation	operator: 33 operands: 34
30	Operation	operator: 35 operands: 36
31	Literal
32	ExprTuple	37, 38
33	Literal
34	ExprTuple	39, 40
35	Literal
36	ExprTuple	56, 41
37	Operation	operator: 44 operands: 42
38	Operation	operator: 44 operands: 43
39	Operation	operator: 44 operands: 45
40	Literal
41	Literal
42	ExprTuple	47, 46, 48
43	ExprTuple	46, 47, 48
44	Literal
45	ExprTuple	47, 48
46	ExprRange	lambda_map: 49 start_index: 54 end_index: 50
47	ExprRange	lambda_map: 51 start_index: 54 end_index: 52
48	ExprRange	lambda_map: 53 start_index: 54 end_index: 55
49	Lambda	parameter: 63 body: 56
50	Variable
51	Lambda	parameter: 63 body: 57
52	Variable
53	Lambda	parameter: 63 body: 58
54	Literal
55	Variable
56	IndexedVar	variable: 59 index: 63
57	IndexedVar	variable: 60 index: 63
58	IndexedVar	variable: 61 index: 63
59	Variable
60	Variable
61	Variable
62	ExprTuple	63
63	Variable