Expression of type Forall

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

# build up the expression from sub-expressions
expr = 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))

expr:

# 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())

\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)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameters: 4 body: 5
4	ExprTuple	42, 35
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operands: 9
7	Operation	operator: 10 operands: 11
8	Literal
9	ExprTuple	12, 13
10	Literal
11	ExprTuple	14, 15, 16
12	Operation	operator: 17 operands: 18
13	Operation	operator: 37 operands: 19
14	Operation	operator: 32 operands: 20
15	ExprRange	lambda_map: 21 start_index: 40 end_index: 41
16	Operation	operator: 22 operands: 23
17	Literal
18	ExprTuple	24
19	ExprTuple	42, 25
20	ExprTuple	42, 26
21	Lambda	parameter: 46 body: 27
22	Literal
23	ExprTuple	42, 28
24	ExprRange	lambda_map: 29 start_index: 40 end_index: 41
25	Operation	operator: 30 operands: 31
26	Literal
27	Operation	operator: 32 operands: 33
28	Literal
29	Lambda	parameter: 46 body: 34
30	Literal
31	ExprTuple	35
32	Literal
33	ExprTuple	43, 36
34	Operation	operator: 37 operands: 38
35	ExprRange	lambda_map: 39 start_index: 40 end_index: 41
36	Literal
37	Literal
38	ExprTuple	42, 43
39	Lambda	parameter: 46 body: 43
40	Literal
41	Variable
42	Variable
43	IndexedVar	variable: 44 index: 46
44	Variable
45	ExprTuple	46
46	Variable