Expression of type Equals

from the theory of proveit.linear_algebra.scalar_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 ExprRange, IndexedVar, Variable
from proveit.linear_algebra import ScalarMult, VecAdd
from proveit.logic import Equals
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Variable("_c", latex_format = r"{_{-}c}")
sub_expr3 = Variable("_d", latex_format = r"{_{-}d}")
sub_expr4 = IndexedVar(Variable("_b", latex_format = r"{_{-}b}"), sub_expr1)
expr = Equals(VecAdd(ExprRange(sub_expr1, ScalarMult(sub_expr2, sub_expr4), one, sub_expr3)), ScalarMult(sub_expr2, VecAdd(ExprRange(sub_expr1, sub_expr4, one, sub_expr3))))

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({_{-}c} \cdot {_{-}b}_{1}\right) +  \left({_{-}c} \cdot {_{-}b}_{2}\right) +  \ldots +  \left({_{-}c} \cdot {_{-}b}_{{_{-}d}}\right)\right) = \left({_{-}c} \cdot \left({_{-}b}_{1} +  {_{-}b}_{2} +  \ldots +  {_{-}b}_{{_{-}d}}\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: 10 operands: 5
4	Operation	operator: 14 operands: 6
5	ExprTuple	7
6	ExprTuple	19, 8
7	ExprRange	lambda_map: 9 start_index: 17 end_index: 18
8	Operation	operator: 10 operands: 11
9	Lambda	parameter: 23 body: 12
10	Literal
11	ExprTuple	13
12	Operation	operator: 14 operands: 15
13	ExprRange	lambda_map: 16 start_index: 17 end_index: 18
14	Literal
15	ExprTuple	19, 20
16	Lambda	parameter: 23 body: 20
17	Literal
18	Variable
19	Variable
20	IndexedVar	variable: 21 index: 23
21	Variable
22	ExprTuple	23
23	Variable