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 B, ExprRange, ExprTuple, IndexedVar, Lambda, Variable, i
from proveit.core_expr_types import A_1_to_m, B_1_to_i, C_1_to_n
from proveit.linear_algebra import VecAdd
from proveit.logic import Equals, Implies, InClass
from proveit.numbers import one
from proveit.physics.quantum import Qmult, QmultCodomain

# build up the expression from sub-expressions
sub_expr1 = Variable("_b", latex_format = r"{_{-}b}")
sub_expr2 = Qmult(A_1_to_m, VecAdd(B_1_to_i), C_1_to_n)
expr = ExprTuple(Lambda([A_1_to_m, B_1_to_i, C_1_to_n], Implies(InClass(sub_expr2, QmultCodomain), Equals(sub_expr2, VecAdd(ExprRange(sub_expr1, Qmult(A_1_to_m, IndexedVar(B, sub_expr1), C_1_to_n), one, i))).with_wrapping_at(2)).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}, B_{1}, B_{2}, \ldots, B_{i}, C_{1}, C_{2}, \ldots, C_{n}\right) \mapsto \left(\begin{array}{c} \begin{array}{l} \left(\left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{m} \thinspace \left(B_{1} +  B_{2} +  \ldots +  B_{i}\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(B_{1} +  B_{2} +  \ldots +  B_{i}\right)\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\right) =  \\ \left(\left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{m} \thinspace B_{1}\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\right) +  \left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{m} \thinspace B_{2}\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\right) +  \ldots +  \left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{m} \thinspace B_{i}\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	29, 22, 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: 26 operands: 15
14	Operation	operator: 19 operands: 16
15	ExprTuple	29, 17, 31
16	ExprTuple	18
17	Operation	operator: 19 operands: 20
18	ExprRange	lambda_map: 21 start_index: 37 end_index: 25
19	Literal
20	ExprTuple	22
21	Lambda	parameter: 40 body: 23
22	ExprRange	lambda_map: 24 start_index: 37 end_index: 25
23	Operation	operator: 26 operands: 27
24	Lambda	parameter: 45 body: 28
25	Variable
26	Literal
27	ExprTuple	29, 30, 31
28	IndexedVar	variable: 34 index: 45
29	ExprRange	lambda_map: 32 start_index: 37 end_index: 33
30	IndexedVar	variable: 34 index: 40
31	ExprRange	lambda_map: 36 start_index: 37 end_index: 38
32	Lambda	parameter: 45 body: 39
33	Variable
34	Variable
35	ExprTuple	40
36	Lambda	parameter: 45 body: 41
37	Literal
38	Variable
39	IndexedVar	variable: 42 index: 45
40	Variable
41	IndexedVar	variable: 43 index: 45
42	Variable
43	Variable
44	ExprTuple	45
45	Variable