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
from proveit.core_expr_types import b_1_to_m
from proveit.logic import Equals, Forall, InSet, NotEquals
from proveit.numbers import Add, Complex, Exp, NaturalPos, Real, zero
from proveit.numbers.exponentiation import prod_a_raise_bi__1_to_m

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [a, b_1_to_m], instance_expr = Equals(prod_a_raise_bi__1_to_m, Exp(a, Add(b_1_to_m))), domains = [Complex, Real], condition = NotEquals(a, zero)), InSet(m, 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\{\forall_{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}~\left(\left(a^{b_{1}} \cdot  a^{b_{2}} \cdot  \ldots \cdot  a^{b_{m}}\right) = a^{b_{1} +  b_{2} +  \ldots +  b_{m}}\right) \textrm{ if } m \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 operand: 6
2	Operation	operator: 36 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	45, 7
6	Lambda	parameters: 8 body: 9
7	Literal
8	ExprTuple	46, 39
9	Conditional	value: 10 condition: 11
10	Operation	operator: 12 operands: 13
11	Operation	operator: 14 operands: 15
12	Literal
13	ExprTuple	16, 17
14	Literal
15	ExprTuple	18, 19, 20
16	Operation	operator: 21 operands: 22
17	Operation	operator: 41 operands: 23
18	Operation	operator: 36 operands: 24
19	ExprRange	lambda_map: 25 start_index: 44 end_index: 45
20	Operation	operator: 26 operands: 27
21	Literal
22	ExprTuple	28
23	ExprTuple	46, 29
24	ExprTuple	46, 30
25	Lambda	parameter: 50 body: 31
26	Literal
27	ExprTuple	46, 32
28	ExprRange	lambda_map: 33 start_index: 44 end_index: 45
29	Operation	operator: 34 operands: 35
30	Literal
31	Operation	operator: 36 operands: 37
32	Literal
33	Lambda	parameter: 50 body: 38
34	Literal
35	ExprTuple	39
36	Literal
37	ExprTuple	47, 40
38	Operation	operator: 41 operands: 42
39	ExprRange	lambda_map: 43 start_index: 44 end_index: 45
40	Literal
41	Literal
42	ExprTuple	46, 47
43	Lambda	parameter: 50 body: 47
44	Literal
45	Variable
46	Variable
47	IndexedVar	variable: 48 index: 50
48	Variable
49	ExprTuple	50
50	Variable

Expression of type Conditional¶

from the theory of proveit.numbers.exponentiation¶

Expression of type Conditional ¶

from the theory of proveit.numbers.exponentiation ¶