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Expression of type Conditional

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, a, m, n
from proveit.logic import And, Equals, InSet
from proveit.numbers import Add, Complex, Exp, Mult, NaturalPos
In [2]:
# build up the expression from sub-expressions
expr = Conditional(Equals(Mult(Exp(a, m), Exp(a, n)), Exp(a, Add(m, n))), And(InSet(a, Complex), InSet(m, NaturalPos), 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\{\left(a^{m} \cdot a^{n}\right) = a^{m + n} \textrm{ if } a \in \mathbb{C} ,  m \in \mathbb{N}^+ ,  n \in \mathbb{N}^+\right..
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 3
operands: 4
2Operationoperator: 5
operands: 6
3Literal
4ExprTuple7, 8
5Literal
6ExprTuple9, 10, 11
7Operationoperator: 12
operands: 13
8Operationoperator: 25
operands: 14
9Operationoperator: 17
operands: 15
10Operationoperator: 17
operands: 16
11Operationoperator: 17
operands: 18
12Literal
13ExprTuple19, 20
14ExprTuple29, 21
15ExprTuple29, 22
16ExprTuple30, 23
17Literal
18ExprTuple31, 23
19Operationoperator: 25
operands: 24
20Operationoperator: 25
operands: 26
21Operationoperator: 27
operands: 28
22Literal
23Literal
24ExprTuple29, 30
25Literal
26ExprTuple29, 31
27Literal
28ExprTuple30, 31
29Variable
30Variable
31Variable