Expression of type Implies

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, ExprRange, IndexedVar, Variable, i
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 Equals, Implies, InClass
from proveit.numbers import 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 = 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)

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())

\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}

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	(2)	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	10, 9
7	Literal
8	ExprTuple	10, 11
9	Literal
10	Operation	operator: 23 operands: 12
11	Operation	operator: 16 operands: 13
12	ExprTuple	26, 14, 28
13	ExprTuple	15
14	Operation	operator: 16 operands: 17
15	ExprRange	lambda_map: 18 start_index: 34 end_index: 22
16	Literal
17	ExprTuple	19
18	Lambda	parameter: 37 body: 20
19	ExprRange	lambda_map: 21 start_index: 34 end_index: 22
20	Operation	operator: 23 operands: 24
21	Lambda	parameter: 42 body: 25
22	Variable
23	Literal
24	ExprTuple	26, 27, 28
25	IndexedVar	variable: 31 index: 42
26	ExprRange	lambda_map: 29 start_index: 34 end_index: 30
27	IndexedVar	variable: 31 index: 37
28	ExprRange	lambda_map: 33 start_index: 34 end_index: 35
29	Lambda	parameter: 42 body: 36
30	Variable
31	Variable
32	ExprTuple	37
33	Lambda	parameter: 42 body: 38
34	Literal
35	Variable
36	IndexedVar	variable: 39 index: 42
37	Variable
38	IndexedVar	variable: 40 index: 42
39	Variable
40	Variable
41	ExprTuple	42
42	Variable