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 B, Conditional, ExprRange, IndexedVar, Lambda, Variable, i, m, n
from proveit.core_expr_types import A_1_to_m, B_1_to_i, C_1_to_n
from proveit.linear_algebra import VecAdd
from proveit.logic import And, Equals, Forall, Implies, InClass, InSet
from proveit.numbers import Natural, NaturalPos, one
from proveit.physics.quantum import Qmult, QmultCodomain

# build up the expression from sub-expressions
sub_expr1 = Variable("_b", latex_format = r"{_{-}b}")
sub_expr2 = Qmult(A_1_to_m, VecAdd(B_1_to_i), C_1_to_n)
expr = Lambda([i, m, n], Conditional(Forall(instance_param_or_params = [A_1_to_m, B_1_to_i, C_1_to_n], instance_expr = Implies(InClass(sub_expr2, QmultCodomain), Equals(sub_expr2, VecAdd(ExprRange(sub_expr1, Qmult(A_1_to_m, IndexedVar(B, sub_expr1), C_1_to_n), one, i))).with_wrapping_at(2)).with_wrapping_at(2)), And(InSet(i, NaturalPos), InSet(m, 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(i, m, n\right) \mapsto \left\{\forall_{A_{1}, A_{2}, \ldots, A_{m}, B_{1}, B_{2}, \ldots, B_{i}, C_{1}, C_{2}, \ldots, C_{n}}~\left(\begin{array}{c} \begin{array}{l} \left(\left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{m} \thinspace \left(B_{1} +  B_{2} +  \ldots +  B_{i}\right)\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\right) \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}\right) \Rightarrow  \\ \left(\begin{array}{c} \begin{array}{l} \left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{m} \thinspace \left(B_{1} +  B_{2} +  \ldots +  B_{i}\right)\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\right) =  \\ \left(\left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{m} \thinspace B_{1}\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\right) +  \left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{m} \thinspace B_{2}\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\right) +  \ldots +  \left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{m} \thinspace B_{i}\thinspace C_{1} \thinspace  C_{2} \thinspace  \ldots \thinspace  C_{n}\right)\right) \end{array} \end{array}\right) \end{array} \end{array}\right) \textrm{ if } i \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	42, 50, 55
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: 13 body: 14
10	Operation	operator: 17 operands: 15
11	Operation	operator: 17 operands: 16
12	Operation	operator: 17 operands: 18
13	ExprTuple	46, 39, 48
14	Operation	operator: 19 operands: 20
15	ExprTuple	42, 21
16	ExprTuple	50, 22
17	Literal
18	ExprTuple	55, 22
19	Literal
20	ExprTuple	23, 24
21	Literal
22	Literal
23	Operation	operator: 25 operands: 26
24	Operation	operator: 27 operands: 28
25	Literal
26	ExprTuple	30, 29
27	Literal
28	ExprTuple	30, 31
29	Literal
30	Operation	operator: 43 operands: 32
31	Operation	operator: 36 operands: 33
32	ExprTuple	46, 34, 48
33	ExprTuple	35
34	Operation	operator: 36 operands: 37
35	ExprRange	lambda_map: 38 start_index: 54 end_index: 42
36	Literal
37	ExprTuple	39
38	Lambda	parameter: 57 body: 40
39	ExprRange	lambda_map: 41 start_index: 54 end_index: 42
40	Operation	operator: 43 operands: 44
41	Lambda	parameter: 62 body: 45
42	Variable
43	Literal
44	ExprTuple	46, 47, 48
45	IndexedVar	variable: 51 index: 62
46	ExprRange	lambda_map: 49 start_index: 54 end_index: 50
47	IndexedVar	variable: 51 index: 57
48	ExprRange	lambda_map: 53 start_index: 54 end_index: 55
49	Lambda	parameter: 62 body: 56
50	Variable
51	Variable
52	ExprTuple	57
53	Lambda	parameter: 62 body: 58
54	Literal
55	Variable
56	IndexedVar	variable: 59 index: 62
57	Variable
58	IndexedVar	variable: 60 index: 62
59	Variable
60	Variable
61	ExprTuple	62
62	Variable