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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, Lambda, b, m
from proveit.core_expr_types import a_1_to_m
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Complex, Exp, Mult, NaturalPos, RealPos
from proveit.numbers.exponentiation import prod_ai_raise_b__1_to_m
In [2]:
# build up the expression from sub-expressions
expr = Lambda(m, Conditional(Forall(instance_param_or_params = [a_1_to_m, b], instance_expr = Equals(Exp(Mult(a_1_to_m), b), prod_ai_raise_b__1_to_m), domains = [Complex, RealPos]), 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())
m \mapsto \left\{\forall_{\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(\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)\right) \textrm{ if } m \in \mathbb{N}^+\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameter: 40
body: 2
1ExprTuple40
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operand: 8
4Operationoperator: 33
operands: 7
5Literal
6ExprTuple8
7ExprTuple40, 9
8Lambdaparameters: 10
body: 11
9Literal
10ExprTuple35, 44
11Conditionalvalue: 12
condition: 13
12Operationoperator: 14
operands: 15
13Operationoperator: 16
operands: 17
14Literal
15ExprTuple18, 19
16Literal
17ExprTuple20, 21
18Operationoperator: 41
operands: 22
19Operationoperator: 30
operands: 23
20ExprRangelambda_map: 24
start_index: 39
end_index: 40
21Operationoperator: 33
operands: 25
22ExprTuple26, 44
23ExprTuple27
24Lambdaparameter: 47
body: 28
25ExprTuple44, 29
26Operationoperator: 30
operands: 31
27ExprRangelambda_map: 32
start_index: 39
end_index: 40
28Operationoperator: 33
operands: 34
29Literal
30Literal
31ExprTuple35
32Lambdaparameter: 47
body: 36
33Literal
34ExprTuple43, 37
35ExprRangelambda_map: 38
start_index: 39
end_index: 40
36Operationoperator: 41
operands: 42
37Literal
38Lambdaparameter: 47
body: 43
39Literal
40Variable
41Literal
42ExprTuple43, 44
43IndexedVarvariable: 45
index: 47
44Variable
45Variable
46ExprTuple47
47Variable