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Expression of type ExprTuple

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, Conditional, ExprTuple, Lambda, m
from proveit.core_expr_types import A_1_to_m
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import NaturalPos
from proveit.physics.quantum import Qmult
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda(m, Conditional(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)), InSet(m, NaturalPos))))
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())
\left(m \mapsto \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) \textrm{ if } m \in \mathbb{N}^+\right..\right)
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0ExprTuple1
1Lambdaparameter: 26
body: 3
2ExprTuple26
3Conditionalvalue: 4
condition: 5
4Operationoperator: 6
operand: 10
5Operationoperator: 8
operands: 9
6Literal
7ExprTuple10
8Literal
9ExprTuple26, 11
10Lambdaparameters: 17
body: 12
11Literal
12Operationoperator: 13
operands: 14
13Literal
14ExprTuple15, 16
15Operationoperator: 21
operands: 17
16Operationoperator: 21
operands: 18
17ExprTuple23, 20
18ExprTuple19, 20
19Operationoperator: 21
operands: 22
20Variable
21Literal
22ExprTuple23
23ExprRangelambda_map: 24
start_index: 25
end_index: 26
24Lambdaparameter: 30
body: 27
25Literal
26Variable
27IndexedVarvariable: 28
index: 30
28Variable
29ExprTuple30
30Variable