Expression of type Equals

from the theory of proveit.core_expr_types.tuples

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, Variable, i, j, k
from proveit.logic import Equals
from proveit.numbers import Add, Exp, e, four, one, three, two

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Equals([ExprRange(sub_expr1, Exp(e, Add(sub_expr1, j)), i, k)], [Exp(e, Add(i, j)), Exp(e, Add(Add(i, one), j)), Exp(e, Add(Add(i, two), j)), Exp(e, Add(Add(i, three), j)), Exp(e, Add(Add(i, four), j))])

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