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Expression of type ExprTuple

from the theory of proveit.numbers.exponentiation

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 Conditional, ExprRange, ExprTuple, IndexedVar, Lambda, Variable, a, b, m
from proveit.core_expr_types import a_1_to_m
from proveit.logic import And, Equals, InSet
from proveit.numbers import Complex, Exp, Mult, RealPos, one
from proveit.numbers.exponentiation import prod_ai_raise_b__1_to_m
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Lambda([a_1_to_m, b], Conditional(Equals(Exp(Mult(a_1_to_m), b), prod_ai_raise_b__1_to_m), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), RealPos), one, m), InSet(b, Complex)))))
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(\left(a_{1}, a_{2}, \ldots, a_{m}, b\right) \mapsto \left\{\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{m}\right)^{b} = \left(\left(a_{1}\right)^{b} \cdot  \left(a_{2}\right)^{b} \cdot  \ldots \cdot  \left(a_{m}\right)^{b}\right) \textrm{ if } \left(a_{1} \in \mathbb{R}^+\right) ,  \left(a_{2} \in \mathbb{R}^+\right) ,  \ldots ,  \left(a_{m} \in \mathbb{R}^+\right) ,  b \in \mathbb{C}\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
1Lambdaparameters: 2
body: 3
2ExprTuple27, 36
3Conditionalvalue: 4
condition: 5
4Operationoperator: 6
operands: 7
5Operationoperator: 8
operands: 9
6Literal
7ExprTuple10, 11
8Literal
9ExprTuple12, 13
10Operationoperator: 33
operands: 14
11Operationoperator: 22
operands: 15
12ExprRangelambda_map: 16
start_index: 31
end_index: 32
13Operationoperator: 25
operands: 17
14ExprTuple18, 36
15ExprTuple19
16Lambdaparameter: 39
body: 20
17ExprTuple36, 21
18Operationoperator: 22
operands: 23
19ExprRangelambda_map: 24
start_index: 31
end_index: 32
20Operationoperator: 25
operands: 26
21Literal
22Literal
23ExprTuple27
24Lambdaparameter: 39
body: 28
25Literal
26ExprTuple35, 29
27ExprRangelambda_map: 30
start_index: 31
end_index: 32
28Operationoperator: 33
operands: 34
29Literal
30Lambdaparameter: 39
body: 35
31Literal
32Variable
33Literal
34ExprTuple35, 36
35IndexedVarvariable: 37
index: 39
36Variable
37Variable
38ExprTuple39
39Variable