Expression of type Equals

from the theory of proveit.numbers.numerals.decimals

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 Function, f, i
from proveit.core_expr_types import f_i_to_j
from proveit.logic import Equals
from proveit.numbers import Add, eight, five, four, one, seven, six, three, two

# build up the expression from sub-expressions
expr = Equals([f_i_to_j], [Function(f, [i]), Function(f, [Add(i, one)]), Function(f, [Add(i, two)]), Function(f, [Add(i, three)]), Function(f, [Add(i, four)]), Function(f, [Add(i, five)]), Function(f, [Add(i, six)]), Function(f, [Add(i, seven)]), Function(f, [Add(i, eight)])])

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(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j\right)\right) = \left(f\left(i\right), f\left(i + 1\right), f\left(i + 2\right), f\left(i + 3\right), f\left(i + 4\right), f\left(i + 5\right), f\left(i + 6\right), f\left(i + 7\right), f\left(i + 8\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	ExprTuple	5
4	ExprTuple	6, 7, 8, 9, 10, 11, 12, 13, 14
5	ExprRange	lambda_map: 15 start_index: 54 end_index: 16
6	Operation	operator: 35 operand: 54
7	Operation	operator: 35 operand: 27
8	Operation	operator: 35 operand: 28
9	Operation	operator: 35 operand: 29
10	Operation	operator: 35 operand: 30
11	Operation	operator: 35 operand: 31
12	Operation	operator: 35 operand: 32
13	Operation	operator: 35 operand: 33
14	Operation	operator: 35 operand: 34
15	Lambda	parameter: 46 body: 26
16	Variable
17	ExprTuple	54
18	ExprTuple	27
19	ExprTuple	28
20	ExprTuple	29
21	ExprTuple	30
22	ExprTuple	31
23	ExprTuple	32
24	ExprTuple	33
25	ExprTuple	34
26	Operation	operator: 35 operand: 46
27	Operation	operator: 44 operands: 37
28	Operation	operator: 44 operands: 38
29	Operation	operator: 44 operands: 39
30	Operation	operator: 44 operands: 40
31	Operation	operator: 44 operands: 41
32	Operation	operator: 44 operands: 42
33	Operation	operator: 44 operands: 43
34	Operation	operator: 44 operands: 45
35	Variable
36	ExprTuple	46
37	ExprTuple	54, 47
38	ExprTuple	54, 48
39	ExprTuple	54, 49
40	ExprTuple	54, 50
41	ExprTuple	54, 51
42	ExprTuple	54, 52
43	ExprTuple	54, 53
44	Literal
45	ExprTuple	54, 55
46	Variable
47	Literal
48	Literal
49	Literal
50	Literal
51	Literal
52	Literal
53	Literal
54	Variable
55	Literal