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
from proveit.numbers import Add, Complex, Exp, RealPos
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 = [RealPos, Complex])

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{R}^+,\left(b_{1} \in \mathbb{C}\right), \left(b_{2} \in \mathbb{C}\right), \ldots, \left(b_{m} \in \mathbb{C}\right)}~\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	38, 31
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
12	Operation	operator: 16 operands: 17
13	Operation	operator: 33 operands: 18
14	Operation	operator: 28 operands: 19
15	ExprRange	lambda_map: 20 start_index: 36 end_index: 37
16	Literal
17	ExprTuple	21
18	ExprTuple	38, 22
19	ExprTuple	38, 23
20	Lambda	parameter: 42 body: 24
21	ExprRange	lambda_map: 25 start_index: 36 end_index: 37
22	Operation	operator: 26 operands: 27
23	Literal
24	Operation	operator: 28 operands: 29
25	Lambda	parameter: 42 body: 30
26	Literal
27	ExprTuple	31
28	Literal
29	ExprTuple	39, 32
30	Operation	operator: 33 operands: 34
31	ExprRange	lambda_map: 35 start_index: 36 end_index: 37
32	Literal
33	Literal
34	ExprTuple	38, 39
35	Lambda	parameter: 42 body: 39
36	Literal
37	Variable
38	Variable
39	IndexedVar	variable: 40 index: 42
40	Variable
41	ExprTuple	42
42	Variable