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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, b, n
from proveit.logic import Equals, Forall, InSet, NotEquals
from proveit.numbers import Complex, Exp, Integer, Mult, Neg, zero
In [2]:
# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [a, b], instance_expr = Equals(Exp(Exp(a, b), Neg(n)), Exp(a, Neg(Mult(b, n)))), domain = Complex, condition = NotEquals(a, zero)), InSet(n, Integer))
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\{\forall_{a, b \in \mathbb{C}~|~a \neq 0}~\left((a^{b})^{-n} = a^{-\left(b \cdot n\right)}\right) \textrm{ if } n \in \mathbb{Z}\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
operand: 6
2Operationoperator: 23
operands: 5
3Literal
4ExprTuple6
5ExprTuple42, 7
6Lambdaparameters: 33
body: 8
7Literal
8Conditionalvalue: 9
condition: 10
9Operationoperator: 11
operands: 12
10Operationoperator: 13
operands: 14
11Literal
12ExprTuple15, 16
13Literal
14ExprTuple17, 18, 19
15Operationoperator: 32
operands: 20
16Operationoperator: 32
operands: 21
17Operationoperator: 23
operands: 22
18Operationoperator: 23
operands: 24
19Operationoperator: 25
operands: 26
20ExprTuple27, 28
21ExprTuple37, 29
22ExprTuple37, 30
23Literal
24ExprTuple41, 30
25Literal
26ExprTuple37, 31
27Operationoperator: 32
operands: 33
28Operationoperator: 35
operand: 42
29Operationoperator: 35
operand: 38
30Literal
31Literal
32Literal
33ExprTuple37, 41
34ExprTuple42
35Literal
36ExprTuple38
37Variable
38Operationoperator: 39
operands: 40
39Literal
40ExprTuple41, 42
41Variable
42Variable