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Expression of type Lambda

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, IndexedVar, Lambda, Variable, a, b, m
from proveit.core_expr_types import a_1_to_m
from proveit.logic import And, Equals, InSet, NotEquals
from proveit.numbers import Complex, Exp, Mult, Real, one, zero
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}")
sub_expr2 = IndexedVar(a, sub_expr1)
expr = 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(sub_expr2, Complex), one, m), InSet(b, Real), ExprRange(sub_expr1, NotEquals(sub_expr2, zero), one, m))))
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(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{C}\right) ,  \left(a_{2} \in \mathbb{C}\right) ,  \ldots ,  \left(a_{m} \in \mathbb{C}\right) ,  b \in \mathbb{R}, \left(a_{1} \neq 0\right) ,  \left(a_{2} \neq 0\right) ,  \ldots ,  \left(a_{m} \neq 0\right)\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameters: 1
body: 2
1ExprTuple31, 41
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operands: 6
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9, 10
7Literal
8ExprTuple11, 12, 13
9Operationoperator: 38
operands: 14
10Operationoperator: 24
operands: 15
11ExprRangelambda_map: 16
start_index: 36
end_index: 37
12Operationoperator: 27
operands: 17
13ExprRangelambda_map: 18
start_index: 36
end_index: 37
14ExprTuple19, 41
15ExprTuple20
16Lambdaparameter: 44
body: 21
17ExprTuple41, 22
18Lambdaparameter: 44
body: 23
19Operationoperator: 24
operands: 25
20ExprRangelambda_map: 26
start_index: 36
end_index: 37
21Operationoperator: 27
operands: 28
22Literal
23Operationoperator: 29
operands: 30
24Literal
25ExprTuple31
26Lambdaparameter: 44
body: 32
27Literal
28ExprTuple40, 33
29Literal
30ExprTuple40, 34
31ExprRangelambda_map: 35
start_index: 36
end_index: 37
32Operationoperator: 38
operands: 39
33Literal
34Literal
35Lambdaparameter: 44
body: 40
36Literal
37Variable
38Literal
39ExprTuple40, 41
40IndexedVarvariable: 42
index: 44
41Variable
42Variable
43ExprTuple44
44Variable