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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, a, b, n
from proveit.logic import And, Equals, InSet
from proveit.numbers import Complex, Exp, Mult, NaturalPos
In [2]:
# build up the expression from sub-expressions
expr = Lambda([a, b, n], Conditional(Equals(Exp(Mult(a, b), n), Mult(Exp(a, n), Exp(b, n))), And(InSet(a, Complex), InSet(b, Complex), InSet(n, 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(a, b, n\right) \mapsto \left\{\left(a \cdot b\right)^{n} = \left(a^{n} \cdot b^{n}\right) \textrm{ if } a \in \mathbb{C} ,  b \in \mathbb{C} ,  n \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
0Lambdaparameters: 1
body: 2
1ExprTuple30, 31, 32
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operands: 6
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9, 10
7Literal
8ExprTuple11, 12, 13
9Operationoperator: 28
operands: 14
10Operationoperator: 25
operands: 15
11Operationoperator: 18
operands: 16
12Operationoperator: 18
operands: 17
13Operationoperator: 18
operands: 19
14ExprTuple20, 32
15ExprTuple21, 22
16ExprTuple30, 23
17ExprTuple31, 23
18Literal
19ExprTuple32, 24
20Operationoperator: 25
operands: 26
21Operationoperator: 28
operands: 27
22Operationoperator: 28
operands: 29
23Literal
24Literal
25Literal
26ExprTuple30, 31
27ExprTuple30, 32
28Literal
29ExprTuple31, 32
30Variable
31Variable
32Variable