Expression of type Equals

from the theory of proveit.numbers.division

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, b, c
from proveit.logic import Equals
from proveit.numbers import Exp, Mult, Neg, four, frac, one, three, two

# build up the expression from sub-expressions
sub_expr1 = Neg(one)
sub_expr2 = Mult(frac(four, three), a, b)
expr = Equals(Mult(sub_expr2, Exp(Mult(frac(two, three), c), sub_expr1)), Mult(sub_expr2, Mult(frac(three, two), Exp(c, 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(\left(\frac{4}{3} \cdot a \cdot b\right) \cdot \left(\frac{2}{3} \cdot c\right)^{-1}\right) = \left(\left(\frac{4}{3} \cdot a \cdot b\right) \cdot \left(\frac{3}{2} \cdot c^{-1}\right)\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: 19 operands: 5
4	Operation	operator: 19 operands: 6
5	ExprTuple	8, 7
6	ExprTuple	8, 9
7	Operation	operator: 23 operands: 10
8	Operation	operator: 19 operands: 11
9	Operation	operator: 19 operands: 12
10	ExprTuple	13, 28
11	ExprTuple	14, 15, 16
12	ExprTuple	17, 18
13	Operation	operator: 19 operands: 20
14	Operation	operator: 29 operands: 21
15	Variable
16	Variable
17	Operation	operator: 29 operands: 22
18	Operation	operator: 23 operands: 24
19	Literal
20	ExprTuple	25, 27
21	ExprTuple	26, 34
22	ExprTuple	34, 33
23	Literal
24	ExprTuple	27, 28
25	Operation	operator: 29 operands: 30
26	Literal
27	Variable
28	Operation	operator: 31 operand: 35
29	Literal
30	ExprTuple	33, 34
31	Literal
32	ExprTuple	35
33	Literal
34	Literal
35	Literal