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
from proveit.core_expr_types import A_1_to_l, b_1_to_j
from proveit.logic import And, Equals, Forall, InClass, InSet
from proveit.numbers import Complex, Mult, Natural, NaturalPos
from proveit.physics.quantum import Qmult, QmultCodomain

# build up the expression from sub-expressions
expr = Lambda([j, l], Conditional(Forall(instance_param_or_params = [b_1_to_j], instance_expr = Forall(instance_param_or_params = [A_1_to_l], instance_expr = Equals(Qmult(b_1_to_j, A_1_to_l), Qmult(Mult(b_1_to_j), A_1_to_l)).with_wrapping_at(2), condition = InClass(Qmult(A_1_to_l), QmultCodomain)), domain = Complex), And(InSet(j, NaturalPos), InSet(l, 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\right) \mapsto \left\{\forall_{b_{1}, b_{2}, \ldots, b_{j} \in \mathbb{C}}~\left[\forall_{A_{1}, A_{2}, \ldots, A_{l}~|~\left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{l}\right) \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}}~\left(\begin{array}{c} \begin{array}{l} \left(b_{1} \thinspace  b_{2} \thinspace  \ldots \thinspace  b_{j}\thinspace A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{l}\right) =  \\ \left(\left(b_{1} \cdot  b_{2} \cdot  \ldots \cdot  b_{j}\right)\thinspace A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{l}\right) \end{array} \end{array}\right)\right] \textrm{ if } j \in \mathbb{N}^+ ,  l \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	53, 48
2	Conditional	value: 3 condition: 4
3	Operation	operator: 17 operand: 7
4	Operation	operator: 19 operands: 6
5	ExprTuple	7
6	ExprTuple	8, 9
7	Lambda	parameters: 46 body: 10
8	Operation	operator: 32 operands: 11
9	Operation	operator: 32 operands: 12
10	Conditional	value: 13 condition: 14
11	ExprTuple	53, 15
12	ExprTuple	48, 16
13	Operation	operator: 17 operand: 21
14	Operation	operator: 19 operands: 20
15	Literal
16	Literal
17	Literal
18	ExprTuple	21
19	Literal
20	ExprTuple	22
21	Lambda	parameters: 42 body: 23
22	ExprRange	lambda_map: 24 start_index: 52 end_index: 53
23	Conditional	value: 25 condition: 26
24	Lambda	parameter: 58 body: 27
25	Operation	operator: 28 operands: 29
26	Operation	operator: 30 operands: 31
27	Operation	operator: 32 operands: 33
28	Literal
29	ExprTuple	34, 35
30	Literal
31	ExprTuple	36, 37
32	Literal
33	ExprTuple	55, 38
34	Operation	operator: 41 operands: 39
35	Operation	operator: 41 operands: 40
36	Operation	operator: 41 operands: 42
37	Literal
38	Literal
39	ExprTuple	49, 44
40	ExprTuple	43, 44
41	Literal
42	ExprTuple	44
43	Operation	operator: 45 operands: 46
44	ExprRange	lambda_map: 47 start_index: 52 end_index: 48
45	Literal
46	ExprTuple	49
47	Lambda	parameter: 58 body: 50
48	Variable
49	ExprRange	lambda_map: 51 start_index: 52 end_index: 53
50	IndexedVar	variable: 54 index: 58
51	Lambda	parameter: 58 body: 55
52	Literal
53	Variable
54	Variable
55	IndexedVar	variable: 56 index: 58
56	Variable
57	ExprTuple	58
58	Variable