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, ExprRange, ExprTuple, IndexedVar, Lambda, Variable, b, j
from proveit.core_expr_types import A_1_to_l, C_1_to_n, b_1_to_j
from proveit.logic import And, Equals, Forall, InClass, InSet
from proveit.numbers import Complex, one
from proveit.physics.quantum import Qmult, QmultCodomain

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Lambda([b_1_to_j], Conditional(Forall(instance_param_or_params = [A_1_to_l, C_1_to_n], instance_expr = Equals(Qmult(A_1_to_l, b_1_to_j, C_1_to_n), Qmult(b_1_to_j, A_1_to_l, C_1_to_n)).with_wrapping_at(2), condition = InClass(Qmult(A_1_to_l, C_1_to_n), QmultCodomain)), And(ExprRange(sub_expr1, InSet(IndexedVar(b, sub_expr1), Complex), one, j)))))

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(b_{1}, b_{2}, \ldots, b_{j}\right) \mapsto \left\{\forall_{A_{1}, A_{2}, \ldots, A_{l}, C_{1}, C_{2}, \ldots, C_{n}~|~\left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{l}\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 b_{1} \thinspace  b_{2} \thinspace  \ldots \thinspace  b_{j}\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\right) =  \\ \left(b_{1} \thinspace  b_{2} \thinspace  \ldots \thinspace  b_{j}\thinspace A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{l}\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\right) \end{array} \end{array}\right) \textrm{ if } \left(b_{1} \in \mathbb{C}\right) \land  \left(b_{2} \in \mathbb{C}\right) \land  \ldots \land  \left(b_{j} \in \mathbb{C}\right)\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	32
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
10	Lambda	parameters: 31 body: 12
11	ExprRange	lambda_map: 13 start_index: 40 end_index: 36
12	Conditional	value: 14 condition: 15
13	Lambda	parameter: 49 body: 16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 19 operands: 20
16	Operation	operator: 21 operands: 22
17	Literal
18	ExprTuple	23, 24
19	Literal
20	ExprTuple	25, 26
21	Literal
22	ExprTuple	42, 27
23	Operation	operator: 30 operands: 28
24	Operation	operator: 30 operands: 29
25	Operation	operator: 30 operands: 31
26	Literal
27	Literal
28	ExprTuple	33, 32, 34
29	ExprTuple	32, 33, 34
30	Literal
31	ExprTuple	33, 34
32	ExprRange	lambda_map: 35 start_index: 40 end_index: 36
33	ExprRange	lambda_map: 37 start_index: 40 end_index: 38
34	ExprRange	lambda_map: 39 start_index: 40 end_index: 41
35	Lambda	parameter: 49 body: 42
36	Variable
37	Lambda	parameter: 49 body: 43
38	Variable
39	Lambda	parameter: 49 body: 44
40	Literal
41	Variable
42	IndexedVar	variable: 45 index: 49
43	IndexedVar	variable: 46 index: 49
44	IndexedVar	variable: 47 index: 49
45	Variable
46	Variable
47	Variable
48	ExprTuple	49
49	Variable