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, Conditional, ExprRange, ExprTuple, IndexedVar, Lambda, Variable, i, m, n
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 And, Equals, Forall, Implies, InClass, InSet
from proveit.numbers import Natural, NaturalPos, 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([i, m, n], Conditional(Forall(instance_param_or_params = [A_1_to_m, B_1_to_i, C_1_to_n], instance_expr = 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)), And(InSet(i, 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(i, m, n\right) \mapsto \left\{\forall_{A_{1}, A_{2}, \ldots, A_{m}, B_{1}, B_{2}, \ldots, B_{i}, C_{1}, C_{2}, \ldots, C_{n}}~\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) \textrm{ if } i \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	43, 51, 56
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	47, 40, 49
15	Operation	operator: 20 operands: 21
16	ExprTuple	43, 22
17	ExprTuple	51, 23
18	Literal
19	ExprTuple	56, 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: 44 operands: 33
32	Operation	operator: 37 operands: 34
33	ExprTuple	47, 35, 49
34	ExprTuple	36
35	Operation	operator: 37 operands: 38
36	ExprRange	lambda_map: 39 start_index: 55 end_index: 43
37	Literal
38	ExprTuple	40
39	Lambda	parameter: 58 body: 41
40	ExprRange	lambda_map: 42 start_index: 55 end_index: 43
41	Operation	operator: 44 operands: 45
42	Lambda	parameter: 63 body: 46
43	Variable
44	Literal
45	ExprTuple	47, 48, 49
46	IndexedVar	variable: 52 index: 63
47	ExprRange	lambda_map: 50 start_index: 55 end_index: 51
48	IndexedVar	variable: 52 index: 58
49	ExprRange	lambda_map: 54 start_index: 55 end_index: 56
50	Lambda	parameter: 63 body: 57
51	Variable
52	Variable
53	ExprTuple	58
54	Lambda	parameter: 63 body: 59
55	Literal
56	Variable
57	IndexedVar	variable: 60 index: 63
58	Variable
59	IndexedVar	variable: 61 index: 63
60	Variable
61	Variable
62	ExprTuple	63
63	Variable