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, 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 = 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(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..

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	37, 45, 39
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	10, 11, 12
9	Lambda	parameters: 30 body: 13
10	Operation	operator: 16 operands: 14
11	Operation	operator: 16 operands: 15
12	Operation	operator: 16 operands: 17
13	Conditional	value: 18 condition: 19
14	ExprTuple	37, 21
15	ExprTuple	45, 20
16	Literal
17	ExprTuple	39, 21
18	Operation	operator: 22 operands: 23
19	Operation	operator: 24 operands: 25
20	Literal
21	Literal
22	Literal
23	ExprTuple	26, 27
24	Literal
25	ExprTuple	27, 28
26	Operation	operator: 34 operands: 29
27	Operation	operator: 34 operands: 30
28	Literal
29	ExprTuple	32, 31, 33
30	ExprTuple	32, 40, 33
31	Operation	operator: 34 operands: 35
32	ExprRange	lambda_map: 36 start_index: 44 end_index: 37
33	ExprRange	lambda_map: 38 start_index: 44 end_index: 39
34	Literal
35	ExprTuple	40
36	Lambda	parameter: 51 body: 41
37	Variable
38	Lambda	parameter: 51 body: 42
39	Variable
40	ExprRange	lambda_map: 43 start_index: 44 end_index: 45
41	IndexedVar	variable: 46 index: 51
42	IndexedVar	variable: 47 index: 51
43	Lambda	parameter: 51 body: 48
44	Literal
45	Variable
46	Variable
47	Variable
48	IndexedVar	variable: 49 index: 51
49	Variable
50	ExprTuple	51
51	Variable