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, Lambda, Q, f
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 Equals, Implies, InClass
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([A_1_to_m, C_1_to_n, f, Q], 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)))

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(A_{1}, A_{2}, \ldots, A_{m}, C_{1}, C_{2}, \ldots, C_{n}, f, Q\right) \mapsto \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)\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	28, 30, 34, 31
3	Operation	operator: 4 operands: 5
4	Literal
5	ExprTuple	6, 7
6	Operation	operator: 8 operands: 9
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	13, 12
10	Literal
11	ExprTuple	13, 14
12	Literal
13	Operation	operator: 25 operands: 15
14	Operation	operator: 19 operand: 18
15	ExprTuple	28, 17, 30
16	ExprTuple	18
17	Operation	operator: 19 operand: 22
18	Lambda	parameters: 35 body: 21
19	Literal
20	ExprTuple	22
21	Conditional	value: 23 condition: 27
22	Lambda	parameters: 35 body: 24
23	Operation	operator: 25 operands: 26
24	Conditional	value: 29 condition: 27
25	Literal
26	ExprTuple	28, 29, 30
27	Operation	operator: 31 operands: 35
28	ExprRange	lambda_map: 32 start_index: 43 end_index: 33
29	Operation	operator: 34 operands: 35
30	ExprRange	lambda_map: 36 start_index: 43 end_index: 37
31	Variable
32	Lambda	parameter: 49 body: 38
33	Variable
34	Variable
35	ExprTuple	39
36	Lambda	parameter: 49 body: 40
37	Variable
38	IndexedVar	variable: 41 index: 49
39	ExprRange	lambda_map: 42 start_index: 43 end_index: 44
40	IndexedVar	variable: 45 index: 49
41	Variable
42	Lambda	parameter: 49 body: 46
43	Literal
44	Variable
45	Variable
46	IndexedVar	variable: 47 index: 49
47	Variable
48	ExprTuple	49
49	Variable