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, Q, f, j, m, n
from proveit.core_expr_types import A_1_to_m, C_1_to_n, Q__b_1_to_j, b_1_to_j, f__b_1_to_j
from proveit.linear_algebra import VecSum
from proveit.linear_algebra.addition import vec_summation_b1toj_fQ
from proveit.logic import And, Equals, Forall, Implies, InClass, InSet
from proveit.numbers import Natural, NaturalPos
from proveit.physics.quantum import Qmult, QmultCodomain

# build up the expression from sub-expressions
sub_expr1 = Qmult(A_1_to_m, vec_summation_b1toj_fQ, C_1_to_n)
expr = ExprTuple(Lambda([j, m, n], Conditional(Forall(instance_param_or_params = [A_1_to_m, C_1_to_n, f, Q], instance_expr = Implies(InClass(sub_expr1, QmultCodomain), Equals(sub_expr1, VecSum(index_or_indices = [b_1_to_j], summand = Qmult(A_1_to_m, f__b_1_to_j, C_1_to_n), condition = Q__b_1_to_j)).with_wrapping_at(1)).with_wrapping_at(2)), And(InSet(j, NaturalPos), InSet(m, 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, m, n\right) \mapsto \left\{\forall_{A_{1}, A_{2}, \ldots, A_{m}, C_{1}, C_{2}, \ldots, C_{n}, f, Q}~\left(\begin{array}{c} \begin{array}{l} \left(\left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{m} \thinspace \left[\sum_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\right]\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\right) \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}\right) \Rightarrow  \\ \left(\begin{array}{c} \begin{array}{l} \left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{m} \thinspace \left[\sum_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\right]\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\right) \\  = \left[\sum_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~\left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{m} \thinspace f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\right)\right] \end{array} \end{array}\right) \end{array} \end{array}\right) \textrm{ if } j \in \mathbb{N}^+ ,  m \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	62, 51, 55
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 10
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	11, 12, 13
10	Lambda	parameters: 14 body: 15
11	Operation	operator: 18 operands: 16
12	Operation	operator: 18 operands: 17
13	Operation	operator: 18 operands: 19
14	ExprTuple	46, 48, 52, 49
15	Operation	operator: 20 operands: 21
16	ExprTuple	62, 22
17	ExprTuple	51, 23
18	Literal
19	ExprTuple	55, 23
20	Literal
21	ExprTuple	24, 25
22	Literal
23	Literal
24	Operation	operator: 26 operands: 27
25	Operation	operator: 28 operands: 29
26	Literal
27	ExprTuple	31, 30
28	Literal
29	ExprTuple	31, 32
30	Literal
31	Operation	operator: 43 operands: 33
32	Operation	operator: 37 operand: 36
33	ExprTuple	46, 35, 48
34	ExprTuple	36
35	Operation	operator: 37 operand: 40
36	Lambda	parameters: 53 body: 39
37	Literal
38	ExprTuple	40
39	Conditional	value: 41 condition: 45
40	Lambda	parameters: 53 body: 42
41	Operation	operator: 43 operands: 44
42	Conditional	value: 47 condition: 45
43	Literal
44	ExprTuple	46, 47, 48
45	Operation	operator: 49 operands: 53
46	ExprRange	lambda_map: 50 start_index: 61 end_index: 51
47	Operation	operator: 52 operands: 53
48	ExprRange	lambda_map: 54 start_index: 61 end_index: 55
49	Variable
50	Lambda	parameter: 67 body: 56
51	Variable
52	Variable
53	ExprTuple	57
54	Lambda	parameter: 67 body: 58
55	Variable
56	IndexedVar	variable: 59 index: 67
57	ExprRange	lambda_map: 60 start_index: 61 end_index: 62
58	IndexedVar	variable: 63 index: 67
59	Variable
60	Lambda	parameter: 67 body: 64
61	Literal
62	Variable
63	Variable
64	IndexedVar	variable: 65 index: 67
65	Variable
66	ExprTuple	67
67	Variable