Expression of type Conditional

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 Conditional, n
from proveit.core_expr_types import Len, i_to_j_len
from proveit.core_expr_types.tuples import f_i_to_j__1_to_n
from proveit.logic import Equals, InSet
from proveit.numbers import Mult, Natural

# build up the expression from sub-expressions
expr = Conditional(Equals(Len(operands = [f_i_to_j__1_to_n]), Mult(n, i_to_j_len)).with_wrapping_at(1), InSet(i_to_j_len, Natural))

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\{\begin{array}{c} \begin{array}{l} |\left(f_{1}\left(i\right), f_{1}\left(i + 1\right), \ldots, f_{1}\left(j\right), f_{2}\left(i\right), f_{2}\left(i + 1\right), \ldots, f_{2}\left(j\right), \ldots\ldots, f_{n}\left(i\right), f_{n}\left(i + 1\right), \ldots, f_{n}\left(j\right)\right)| \\  = \left(n \cdot \left(j - i + 1\right)\right) \end{array} \end{array} \textrm{ if } \left(j - i + 1\right) \in \mathbb{N}\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: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	15, 9
7	Operation	operator: 10 operands: 11
8	Operation	operator: 12 operands: 13
9	Literal
10	Literal
11	ExprTuple	14
12	Literal
13	ExprTuple	17, 15
14	ExprRange	lambda_map: 16 start_index: 22 end_index: 17
15	Operation	operator: 18 operands: 19
16	Lambda	parameter: 34 body: 20
17	Variable
18	Literal
19	ExprTuple	24, 21, 22
20	ExprRange	lambda_map: 23 start_index: 28 end_index: 24
21	Operation	operator: 25 operand: 28
22	Literal
23	Lambda	parameter: 33 body: 27
24	Variable
25	Literal
26	ExprTuple	28
27	Operation	operator: 29 operand: 33
28	Variable
29	IndexedVar	variable: 31 index: 34
30	ExprTuple	33
31	Variable
32	ExprTuple	34
33	Variable
34	Variable