Expression of type Conditional ¶

from the theory of proveit.numbers.exponentiation ¶

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

# 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)))

# 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

# 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..

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10, 11
7	Operation	operator: 12 operands: 13
8	Operation	operator: 25 operands: 14
9	Operation	operator: 17 operands: 15
10	Operation	operator: 17 operands: 16
11	Operation	operator: 17 operands: 18
12	Literal
13	ExprTuple	19, 20
14	ExprTuple	29, 21
15	ExprTuple	29, 22
16	ExprTuple	30, 23
17	Literal
18	ExprTuple	31, 23
19	Operation	operator: 25 operands: 24
20	Operation	operator: 25 operands: 26
21	Operation	operator: 27 operands: 28
22	Literal
23	Literal
24	ExprTuple	29, 30
25	Literal
26	ExprTuple	29, 31
27	Literal
28	ExprTuple	30, 31
29	Variable
30	Variable
31	Variable

Expression of type Conditional¶

from the theory of proveit.numbers.exponentiation¶

Expression of type Conditional ¶

from the theory of proveit.numbers.exponentiation ¶