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, l, m, n
from proveit.core_expr_types import A_1_to_l, B_1_to_m, C_1_to_n
from proveit.logic import And, Equals, Forall, 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_l, B_1_to_m, C_1_to_n)
expr = ExprTuple(Lambda([l, m, n], Conditional(Forall(instance_param_or_params = [A_1_to_l, B_1_to_m, C_1_to_n], instance_expr = Equals(Qmult(A_1_to_l, Qmult(B_1_to_m), C_1_to_n), sub_expr1).with_wrapping_at(2), condition = InClass(sub_expr1, QmultCodomain)), And(InSet(l, Natural), InSet(m, NaturalPos), 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(l, m, n\right) \mapsto \left\{\forall_{A_{1}, A_{2}, \ldots, A_{l}, B_{1}, B_{2}, \ldots, B_{m}, C_{1}, C_{2}, \ldots, C_{n}~|~\left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{l}\thinspace B_{1} \thinspace  B_{2} \thinspace  \ldots \thinspace  B_{m}\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\right) \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}}~\left(\begin{array}{c} \begin{array}{l} \left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{l} \thinspace \left(B_{1} \thinspace  B_{2} \thinspace  \ldots \thinspace  B_{m}\right)\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\right) =  \\ \left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{l}\thinspace B_{1} \thinspace  B_{2} \thinspace  \ldots \thinspace  B_{m}\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\right) \end{array} \end{array}\right) \textrm{ if } l \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	38, 46, 40
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: 31 body: 14
11	Operation	operator: 17 operands: 15
12	Operation	operator: 17 operands: 16
13	Operation	operator: 17 operands: 18
14	Conditional	value: 19 condition: 20
15	ExprTuple	38, 22
16	ExprTuple	46, 21
17	Literal
18	ExprTuple	40, 22
19	Operation	operator: 23 operands: 24
20	Operation	operator: 25 operands: 26
21	Literal
22	Literal
23	Literal
24	ExprTuple	27, 28
25	Literal
26	ExprTuple	28, 29
27	Operation	operator: 35 operands: 30
28	Operation	operator: 35 operands: 31
29	Literal
30	ExprTuple	33, 32, 34
31	ExprTuple	33, 41, 34
32	Operation	operator: 35 operands: 36
33	ExprRange	lambda_map: 37 start_index: 45 end_index: 38
34	ExprRange	lambda_map: 39 start_index: 45 end_index: 40
35	Literal
36	ExprTuple	41
37	Lambda	parameter: 52 body: 42
38	Variable
39	Lambda	parameter: 52 body: 43
40	Variable
41	ExprRange	lambda_map: 44 start_index: 45 end_index: 46
42	IndexedVar	variable: 47 index: 52
43	IndexedVar	variable: 48 index: 52
44	Lambda	parameter: 52 body: 49
45	Literal
46	Variable
47	Variable
48	Variable
49	IndexedVar	variable: 50 index: 52
50	Variable
51	ExprTuple	52
52	Variable