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 a, b, c, d, x, y
from proveit.logic import Equals
from proveit.numbers import Mult, subtract

# build up the expression from sub-expressions
expr = Equals(Mult(a, b, subtract(x, y), c, d), Mult(subtract(Mult(a, d, x, b), Mult(a, d, y, b)), c))

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 \cdot b \cdot \left(x - y\right) \cdot c \cdot d\right) = \left(\left(\left(a \cdot d \cdot x \cdot b\right) - \left(a \cdot d \cdot y \cdot b\right)\right) \cdot c\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: 22 operands: 5
4	Operation	operator: 22 operands: 6
5	ExprTuple	24, 27, 7, 9, 25
6	ExprTuple	8, 9
7	Operation	operator: 11 operands: 10
8	Operation	operator: 11 operands: 12
9	Variable
10	ExprTuple	20, 13
11	Literal
12	ExprTuple	14, 15
13	Operation	operator: 18 operand: 26
14	Operation	operator: 22 operands: 17
15	Operation	operator: 18 operand: 21
16	ExprTuple	26
17	ExprTuple	24, 25, 20, 27
18	Literal
19	ExprTuple	21
20	Variable
21	Operation	operator: 22 operands: 23
22	Literal
23	ExprTuple	24, 25, 26, 27
24	Variable
25	Variable
26	Variable
27	Variable