Expression of type Equals

from the theory of proveit.numbers.multiplication

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.logic import Equals
from proveit.numbers import Add, Exp, Mult, five, four, frac, one, three, two

# build up the expression from sub-expressions
sub_expr1 = frac(one, five)
expr = Equals(Mult(four, Exp(three, n), Exp(four, n), two, three, sub_expr1), Mult(Exp(four, Add(one, n)), Exp(three, Add(n, one)), two, sub_expr1))

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(4 \cdot 3^{n} \cdot 4^{n} \cdot 2 \cdot 3 \cdot \frac{1}{5}\right) = \left(4^{1 + n} \cdot 3^{n + 1} \cdot 2 \cdot \frac{1}{5}\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: 6 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	21, 8, 9, 12, 23, 13
6	Literal
7	ExprTuple	10, 11, 12, 13
8	Operation	operator: 17 operands: 14
9	Operation	operator: 17 operands: 15
10	Operation	operator: 17 operands: 16
11	Operation	operator: 17 operands: 18
12	Literal
13	Operation	operator: 19 operands: 20
14	ExprTuple	23, 29
15	ExprTuple	21, 29
16	ExprTuple	21, 22
17	Literal
18	ExprTuple	23, 24
19	Literal
20	ExprTuple	30, 25
21	Literal
22	Operation	operator: 27 operands: 26
23	Literal
24	Operation	operator: 27 operands: 28
25	Literal
26	ExprTuple	30, 29
27	Literal
28	ExprTuple	29, 30
29	Variable
30	Literal