# 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.
# import Expression classes needed to build the expression
from proveit import B, m
from proveit.core_expr_types import A_1_to_m
from proveit.logic import Equals, Forall
from proveit.numbers import NaturalPos
from proveit.physics.quantum import Qmult

In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [m], instance_expr = Forall(instance_param_or_params = [A_1_to_m, B], instance_expr = Equals(Qmult(A_1_to_m, B), Qmult(Qmult(A_1_to_m), B)).with_wrapping_at(2)), domain = NaturalPos)

Out[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())

\forall_{m \in \mathbb{N}^+}~\left[\forall_{A_{1}, A_{2}, \ldots, A_{m}, B}~\left(\begin{array}{c} \begin{array}{l} \left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{m} \thinspace B\right) =  \\ \left(\left(A_{1} \thinspace  A_{2} \thinspace  \ldots \thinspace  A_{m}\right) \thinspace B\right) \end{array} \end{array}\right)\right]

In [5]:
stored_expr.style_options()

Out[5]:
namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
condition_wrappingWrap 'before' or 'after' the condition (or None).NoneNone/False('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_paramsIf 'True', wraps every two parameters AND wraps the Expression after the parametersNoneNone/False('with_params',)
justificationjustify to the 'left', 'center', or 'right' in the array cellscentercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()

Out[6]:
core typesub-expressionsexpression
0Operationoperator: 7
operand: 2
1ExprTuple2
2Lambdaparameter: 27
body: 4
3ExprTuple27
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 11
6Operationoperator: 9
operands: 10
7Literal
8ExprTuple11
9Literal
10ExprTuple27, 12
11Lambdaparameters: 18
body: 13
12Literal
13Operationoperator: 14
operands: 15
14Literal
15ExprTuple16, 17
16Operationoperator: 22
operands: 18
17Operationoperator: 22
operands: 19
18ExprTuple24, 21
19ExprTuple20, 21
20Operationoperator: 22
operands: 23
21Variable
22Literal
23ExprTuple24
24ExprRangelambda_map: 25
start_index: 26
end_index: 27
25Lambdaparameter: 31
body: 28
26Literal
27Variable
28IndexedVarvariable: 29
index: 31
29Variable
30ExprTuple31
31Variable