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Expression of type Implies

from the theory of proveit.physics.quantum.algebra

In [1]:
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
In [2]:
# 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:
In [3]:
# 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
In [4]:
# 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}
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(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')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Operationoperator: 5
operands: 6
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple10, 9
7Literal
8ExprTuple10, 11
9Literal
10Operationoperator: 27
operands: 12
11Operationoperator: 17
operands: 13
12ExprTuple22, 23, 24, 14
13ExprTuple15, 16
14Operationoperator: 17
operands: 18
15Operationoperator: 27
operands: 19
16Operationoperator: 27
operands: 20
17Literal
18ExprTuple21, 25
19ExprTuple22, 23, 24, 21
20ExprTuple22, 23, 24, 25
21Operationoperator: 32
operand: 29
22Variable
23Variable
24Variable
25Operationoperator: 27
operands: 28
26ExprTuple29
27Literal
28ExprTuple30, 31
29Variable
30Variable
31Operationoperator: 32
operand: 34
32Literal
33ExprTuple34
34Variable