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 A, D, alpha, beta
from proveit.linear_algebra import VecAdd
from proveit.logic import Equals, Implies, InClass
from proveit.physics.quantum import Qmult, QmultCodomain, ket_psi, ket_varphi

# build up the expression from sub-expressions
sub_expr1 = Qmult(D, ket_varphi)
sub_expr2 = Qmult(alpha, A, beta, VecAdd(ket_psi, sub_expr1))
expr = Implies(InClass(sub_expr2, QmultCodomain), Equals(sub_expr2, VecAdd(Qmult(alpha, A, beta, ket_psi), Qmult(alpha, A, beta, sub_expr1))).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(\alpha \thinspace A \thinspace \beta \thinspace \left(\lvert \psi \rangle + \left(D \thinspace \lvert \varphi \rangle\right)\right)\right) \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}\right) \Rightarrow  \\ \left(\begin{array}{c} \begin{array}{l} \left(\alpha \thinspace A \thinspace \beta \thinspace \left(\lvert \psi \rangle + \left(D \thinspace \lvert \varphi \rangle\right)\right)\right) =  \\ \left(\left(\alpha \thinspace A \thinspace \beta \thinspace \lvert \psi \rangle\right) + \left(\alpha \thinspace A \thinspace \beta \thinspace \left(D \thinspace \lvert \varphi \rangle\right)\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: 27 operands: 12
11	Operation	operator: 17 operands: 13
12	ExprTuple	22, 23, 24, 14
13	ExprTuple	15, 16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 27 operands: 19
16	Operation	operator: 27 operands: 20
17	Literal
18	ExprTuple	21, 25
19	ExprTuple	22, 23, 24, 21
20	ExprTuple	22, 23, 24, 25
21	Operation	operator: 32 operand: 29
22	Variable
23	Variable
24	Variable
25	Operation	operator: 27 operands: 28
26	ExprTuple	29
27	Literal
28	ExprTuple	30, 31
29	Variable
30	Variable
31	Operation	operator: 32 operand: 34
32	Literal
33	ExprTuple	34
34	Variable