Expression of type Equals

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 n
from proveit.core_expr_types import a_1_to_m
from proveit.logic import Equals
from proveit.numbers import Exp, Mult
from proveit.numbers.exponentiation import prod_ai_raise_n__1_to_m

# build up the expression from sub-expressions
expr = Equals(Exp(Mult(a_1_to_m), n), prod_ai_raise_n__1_to_m)

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())

\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{m}\right)^{n} = \left(\left(a_{1}\right)^{n} \cdot  \left(a_{2}\right)^{n} \cdot  \ldots \cdot  \left(a_{m}\right)^{n}\right)

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 17 operands: 5
4	Operation	operator: 9 operands: 6
5	ExprTuple	7, 20
6	ExprTuple	8
7	Operation	operator: 9 operands: 10
8	ExprRange	lambda_map: 11 start_index: 15 end_index: 16
9	Literal
10	ExprTuple	12
11	Lambda	parameter: 23 body: 13
12	ExprRange	lambda_map: 14 start_index: 15 end_index: 16
13	Operation	operator: 17 operands: 18
14	Lambda	parameter: 23 body: 19
15	Literal
16	Variable
17	Literal
18	ExprTuple	19, 20
19	IndexedVar	variable: 21 index: 23
20	Variable
21	Variable
22	ExprTuple	23
23	Variable