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.
# import Expression classes needed to build the expression
from proveit import Conditional, Lambda, a, b, c
from proveit.logic import And, Equals, InSet, NotEquals
from proveit.numbers import Add, Complex, Exp, Mult, Real, zero

In [2]:
# build up the expression from sub-expressions
expr = Lambda([a, b, c], Conditional(Equals(Mult(Exp(a, b), Exp(a, c)), Exp(a, Add(b, c))), And(InSet(a, Complex), InSet(b, Real), InSet(c, Real), NotEquals(a, zero))))

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, c\right) \mapsto \left\{\left(a^{b} \cdot a^{c}\right) = a^{b + c} \textrm{ if } a \in \mathbb{C} ,  b \in \mathbb{R} ,  c \in \mathbb{R} ,  a \neq 0\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
1ExprTuple35, 36, 37
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operands: 6
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9, 10
7Literal
8ExprTuple11, 12, 13, 14
9Operationoperator: 15
operands: 16
10Operationoperator: 31
operands: 17
11Operationoperator: 20
operands: 18
12Operationoperator: 20
operands: 19
13Operationoperator: 20
operands: 21
14Operationoperator: 22
operands: 23
15Literal
16ExprTuple24, 25
17ExprTuple35, 26
18ExprTuple35, 27
19ExprTuple36, 28
20Literal
21ExprTuple37, 28
22Literal
23ExprTuple35, 29
24Operationoperator: 31
operands: 30
25Operationoperator: 31
operands: 32
26Operationoperator: 33
operands: 34
27Literal
28Literal
29Literal
30ExprTuple35, 36
31Literal
32ExprTuple35, 37
33Literal
34ExprTuple36, 37
35Variable
36Variable
37Variable