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Expression of type Forall

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 B
from proveit.core_expr_types import A_1_to_m
from proveit.logic import Equals, Forall
from proveit.physics.quantum import Qmult
In [2]:
# build up the expression from sub-expressions
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))
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_{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)
In [5]:
stored_expr.style_options()
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()
 core typesub-expressionsexpression
0Operationoperator: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameters: 9
body: 4
4Operationoperator: 5
operands: 6
5Literal
6ExprTuple7, 8
7Operationoperator: 13
operands: 9
8Operationoperator: 13
operands: 10
9ExprTuple15, 12
10ExprTuple11, 12
11Operationoperator: 13
operands: 14
12Variable
13Literal
14ExprTuple15
15ExprRangelambda_map: 16
start_index: 17
end_index: 18
16Lambdaparameter: 22
body: 19
17Literal
18Variable
19IndexedVarvariable: 20
index: 22
20Variable
21ExprTuple22
22Variable