Expression of type Conditional

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

# build up the expression from sub-expressions
sub_expr1 = Add(i, seven)
expr = Conditional(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, [sub_expr1])]), Equals(j, 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(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)\right) \textrm{ if } j = \left(i + 7\right)\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 4 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	18, 34
6	ExprTuple	8
7	ExprTuple	9, 10, 11, 12, 13, 14, 15, 16
8	ExprRange	lambda_map: 17 start_index: 52 end_index: 18
9	Operation	operator: 35 operand: 52
10	Operation	operator: 35 operand: 28
11	Operation	operator: 35 operand: 29
12	Operation	operator: 35 operand: 30
13	Operation	operator: 35 operand: 31
14	Operation	operator: 35 operand: 32
15	Operation	operator: 35 operand: 33
16	Operation	operator: 35 operand: 34
17	Lambda	parameter: 45 body: 27
18	Variable
19	ExprTuple	52
20	ExprTuple	28
21	ExprTuple	29
22	ExprTuple	30
23	ExprTuple	31
24	ExprTuple	32
25	ExprTuple	33
26	ExprTuple	34
27	Operation	operator: 35 operand: 45
28	Operation	operator: 43 operands: 37
29	Operation	operator: 43 operands: 38
30	Operation	operator: 43 operands: 39
31	Operation	operator: 43 operands: 40
32	Operation	operator: 43 operands: 41
33	Operation	operator: 43 operands: 42
34	Operation	operator: 43 operands: 44
35	Variable
36	ExprTuple	45
37	ExprTuple	52, 46
38	ExprTuple	52, 47
39	ExprTuple	52, 48
40	ExprTuple	52, 49
41	ExprTuple	52, 50
42	ExprTuple	52, 51
43	Literal
44	ExprTuple	52, 53
45	Variable
46	Literal
47	Literal
48	Literal
49	Literal
50	Literal
51	Literal
52	Variable
53	Literal