Expression of type Lambda

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, Lambda, j, l, n
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, Natural
from proveit.physics.quantum import Qmult, QmultCodomain

# build up the expression from sub-expressions
expr = Lambda([j, l, n], Conditional(Forall(instance_param_or_params = [b_1_to_j], instance_expr = 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)), domain = Complex), And(InSet(j, Natural), InSet(l, 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(j, l, n\right) \mapsto \left\{\forall_{b_{1}, b_{2}, \ldots, b_{j} \in \mathbb{C}}~\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)\right] \textrm{ if } j \in \mathbb{N} ,  l \in \mathbb{N} ,  n \in \mathbb{N}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	49, 51, 54
2	Conditional	value: 3 condition: 4
3	Operation	operator: 19 operand: 7
4	Operation	operator: 21 operands: 6
5	ExprTuple	7
6	ExprTuple	8, 9, 10
7	Lambda	parameters: 11 body: 12
8	Operation	operator: 34 operands: 13
9	Operation	operator: 34 operands: 14
10	Operation	operator: 34 operands: 15
11	ExprTuple	45
12	Conditional	value: 16 condition: 17
13	ExprTuple	49, 18
14	ExprTuple	51, 18
15	ExprTuple	54, 18
16	Operation	operator: 19 operand: 23
17	Operation	operator: 21 operands: 22
18	Literal
19	Literal
20	ExprTuple	23
21	Literal
22	ExprTuple	24
23	Lambda	parameters: 44 body: 25
24	ExprRange	lambda_map: 26 start_index: 53 end_index: 49
25	Conditional	value: 27 condition: 28
26	Lambda	parameter: 62 body: 29
27	Operation	operator: 30 operands: 31
28	Operation	operator: 32 operands: 33
29	Operation	operator: 34 operands: 35
30	Literal
31	ExprTuple	36, 37
32	Literal
33	ExprTuple	38, 39
34	Literal
35	ExprTuple	55, 40
36	Operation	operator: 43 operands: 41
37	Operation	operator: 43 operands: 42
38	Operation	operator: 43 operands: 44
39	Literal
40	Literal
41	ExprTuple	46, 45, 47
42	ExprTuple	45, 46, 47
43	Literal
44	ExprTuple	46, 47
45	ExprRange	lambda_map: 48 start_index: 53 end_index: 49
46	ExprRange	lambda_map: 50 start_index: 53 end_index: 51
47	ExprRange	lambda_map: 52 start_index: 53 end_index: 54
48	Lambda	parameter: 62 body: 55
49	Variable
50	Lambda	parameter: 62 body: 56
51	Variable
52	Lambda	parameter: 62 body: 57
53	Literal
54	Variable
55	IndexedVar	variable: 58 index: 62
56	IndexedVar	variable: 59 index: 62
57	IndexedVar	variable: 60 index: 62
58	Variable
59	Variable
60	Variable
61	ExprTuple	62
62	Variable