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, ExprRange, IndexedVar, Variable, a, b, m
from proveit.core_expr_types import b_1_to_m
from proveit.logic import And, Equals, InSet, NotEquals
from proveit.numbers import Add, Complex, Exp, Real, one, zero
from proveit.numbers.exponentiation import prod_a_raise_bi__1_to_m

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(Equals(prod_a_raise_bi__1_to_m, Exp(a, Add(b_1_to_m))), And(InSet(a, Complex), ExprRange(sub_expr1, InSet(IndexedVar(b, sub_expr1), Real), one, m), NotEquals(a, zero)))

# 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^{b_{1}} \cdot  a^{b_{2}} \cdot  \ldots \cdot  a^{b_{m}}\right) = a^{b_{1} +  b_{2} +  \ldots +  b_{m}} \textrm{ if } a \in \mathbb{C}, \left(b_{1} \in \mathbb{R}\right) ,  \left(b_{2} \in \mathbb{R}\right) ,  \ldots ,  \left(b_{m} \in \mathbb{R}\right) ,  a \neq 0\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: 32 operands: 14
9	Operation	operator: 27 operands: 15
10	ExprRange	lambda_map: 16 start_index: 35 end_index: 36
11	Operation	operator: 17 operands: 18
12	Literal
13	ExprTuple	19
14	ExprTuple	37, 20
15	ExprTuple	37, 21
16	Lambda	parameter: 41 body: 22
17	Literal
18	ExprTuple	37, 23
19	ExprRange	lambda_map: 24 start_index: 35 end_index: 36
20	Operation	operator: 25 operands: 26
21	Literal
22	Operation	operator: 27 operands: 28
23	Literal
24	Lambda	parameter: 41 body: 29
25	Literal
26	ExprTuple	30
27	Literal
28	ExprTuple	38, 31
29	Operation	operator: 32 operands: 33
30	ExprRange	lambda_map: 34 start_index: 35 end_index: 36
31	Literal
32	Literal
33	ExprTuple	37, 38
34	Lambda	parameter: 41 body: 38
35	Literal
36	Variable
37	Variable
38	IndexedVar	variable: 39 index: 41
39	Variable
40	ExprTuple	41
41	Variable

Expression of type Conditional¶

from the theory of proveit.numbers.exponentiation¶

Expression of type Conditional ¶

from the theory of proveit.numbers.exponentiation ¶