logo

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 Complex, Exp, Mult, NaturalPos
In [2]:
# build up the expression from sub-expressions
expr = Conditional(Equals(Exp(Exp(a, m), n), Exp(a, Mult(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\{(a^{m})^{n} = a^{m \cdot 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: 22
operands: 12
8Operationoperator: 22
operands: 13
9Operationoperator: 16
operands: 14
10Operationoperator: 16
operands: 15
11Operationoperator: 16
operands: 17
12ExprTuple18, 28
13ExprTuple26, 19
14ExprTuple26, 20
15ExprTuple27, 21
16Literal
17ExprTuple28, 21
18Operationoperator: 22
operands: 23
19Operationoperator: 24
operands: 25
20Literal
21Literal
22Literal
23ExprTuple26, 27
24Literal
25ExprTuple27, 28
26Variable
27Variable
28Variable