# 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 a, b, c
from proveit.logic import Equals, Forall, NotEquals
from proveit.numbers import Add, Complex, Exp, Mult, Real, zero

In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a, b, c], instance_expr = Equals(Mult(Exp(a, b), Exp(a, c)), Exp(a, Add(b, c))), domains = [Complex, Real, Real], condition = 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())

\forall_{a \in \mathbb{C}, b \in \mathbb{R}, c \in \mathbb{R}~|~a \neq 0}~\left(\left(a^{b} \cdot a^{c}\right) = a^{b + c}\right)

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
condition_wrappingWrap 'before' or 'after' the condition (or None).NoneNone/False('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_paramsIf 'True', wraps every two parameters AND wraps the Expression after the parametersNoneNone/False('with_params',)
justificationjustify to the 'left', 'center', or 'right' in the array cellscentercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Operationoperator: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameters: 4
body: 5
4ExprTuple38, 39, 40
5Conditionalvalue: 6
condition: 7
6Operationoperator: 8
operands: 9
7Operationoperator: 10
operands: 11
8Literal
9ExprTuple12, 13
10Literal
11ExprTuple14, 15, 16, 17
12Operationoperator: 18
operands: 19
13Operationoperator: 34
operands: 20
14Operationoperator: 23
operands: 21
15Operationoperator: 23
operands: 22
16Operationoperator: 23
operands: 24
17Operationoperator: 25
operands: 26
18Literal
19ExprTuple27, 28
20ExprTuple38, 29
21ExprTuple38, 30
22ExprTuple39, 31
23Literal
24ExprTuple40, 31
25Literal
26ExprTuple38, 32
27Operationoperator: 34
operands: 33
28Operationoperator: 34
operands: 35
29Operationoperator: 36
operands: 37
30Literal
31Literal
32Literal
33ExprTuple38, 39
34Literal
35ExprTuple38, 40
36Literal
37ExprTuple39, 40
38Variable
39Variable
40Variable