Expression of type Conditional

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, 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 = 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\{\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()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

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