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
from proveit.core_expr_types import A_1_to_l, b_1_to_j
from proveit.logic import And, Equals, Forall, InClass, InSet
from proveit.numbers import Complex, Mult, Natural, NaturalPos
from proveit.physics.quantum import Qmult, QmultCodomain

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([j, l], Conditional(Forall(instance_param_or_params = [b_1_to_j], instance_expr = Forall(instance_param_or_params = [A_1_to_l], instance_expr = Equals(Qmult(b_1_to_j, A_1_to_l), Qmult(Mult(b_1_to_j), A_1_to_l)).with_wrapping_at(2), condition = InClass(Qmult(A_1_to_l), QmultCodomain)), domain = Complex), And(InSet(j, NaturalPos), InSet(l, 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\right) \mapsto \left\{\forall_{b_{1}, b_{2}, \ldots, b_{j} \in \mathbb{C}}~\left[\forall_{A_{1}, A_{2}, \ldots, A_{l}~|~\left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{l}\right) \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}}~\left(\begin{array}{c} \begin{array}{l} \left(b_{1} \thinspace  b_{2} \thinspace  \ldots \thinspace  b_{j}\thinspace A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{l}\right) =  \\ \left(\left(b_{1} \cdot  b_{2} \cdot  \ldots \cdot  b_{j}\right)\thinspace A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{l}\right) \end{array} \end{array}\right)\right] \textrm{ if } j \in \mathbb{N}^+ ,  l \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	54, 49
3	Conditional	value: 4 condition: 5
4	Operation	operator: 18 operand: 8
5	Operation	operator: 20 operands: 7
6	ExprTuple	8
7	ExprTuple	9, 10
8	Lambda	parameters: 47 body: 11
9	Operation	operator: 33 operands: 12
10	Operation	operator: 33 operands: 13
11	Conditional	value: 14 condition: 15
12	ExprTuple	54, 16
13	ExprTuple	49, 17
14	Operation	operator: 18 operand: 22
15	Operation	operator: 20 operands: 21
16	Literal
17	Literal
18	Literal
19	ExprTuple	22
20	Literal
21	ExprTuple	23
22	Lambda	parameters: 43 body: 24
23	ExprRange	lambda_map: 25 start_index: 53 end_index: 54
24	Conditional	value: 26 condition: 27
25	Lambda	parameter: 59 body: 28
26	Operation	operator: 29 operands: 30
27	Operation	operator: 31 operands: 32
28	Operation	operator: 33 operands: 34
29	Literal
30	ExprTuple	35, 36
31	Literal
32	ExprTuple	37, 38
33	Literal
34	ExprTuple	56, 39
35	Operation	operator: 42 operands: 40
36	Operation	operator: 42 operands: 41
37	Operation	operator: 42 operands: 43
38	Literal
39	Literal
40	ExprTuple	50, 45
41	ExprTuple	44, 45
42	Literal
43	ExprTuple	45
44	Operation	operator: 46 operands: 47
45	ExprRange	lambda_map: 48 start_index: 53 end_index: 49
46	Literal
47	ExprTuple	50
48	Lambda	parameter: 59 body: 51
49	Variable
50	ExprRange	lambda_map: 52 start_index: 53 end_index: 54
51	IndexedVar	variable: 55 index: 59
52	Lambda	parameter: 59 body: 56
53	Literal
54	Variable
55	Variable
56	IndexedVar	variable: 57 index: 59
57	Variable
58	ExprTuple	59
59	Variable