Expression of type Conditional

from the theory of proveit.numbers.number_sets.integers

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, a, b
from proveit.logic import And, Card, Equals, InSet
from proveit.numbers import Add, Integer, Interval, LessEq, Neg, one

# build up the expression from sub-expressions
expr = Conditional(Equals(Card(Interval(a, b)), Add(b, Neg(a), one)), And(InSet(a, Integer), InSet(b, Integer), LessEq(a, b)))

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\{|\{a~\ldotp \ldotp~b\}| = \left(b - a + 1\right) \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z} ,  a \leq b\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	9, 10, 11
7	Operation	operator: 12 operand: 20
8	Operation	operator: 14 operands: 15
9	Operation	operator: 17 operands: 16
10	Operation	operator: 17 operands: 18
11	Operation	operator: 19 operands: 25
12	Literal
13	ExprTuple	20
14	Literal
15	ExprTuple	28, 21, 22
16	ExprTuple	29, 23
17	Literal
18	ExprTuple	28, 23
19	Literal
20	Operation	operator: 24 operands: 25
21	Operation	operator: 26 operand: 29
22	Literal
23	Literal
24	Literal
25	ExprTuple	29, 28
26	Literal
27	ExprTuple	29
28	Variable
29	Variable