Expression of type ExprTuple

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, ExprTuple, Lambda, 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 = ExprTuple(Lambda([a, b], 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(\left(a, b\right) \mapsto \left\{|\{a~\ldotp \ldotp~b\}| = \left(b - a + 1\right) \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z} ,  a \leq b\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 27 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12, 13
9	Operation	operator: 14 operand: 22
10	Operation	operator: 16 operands: 17
11	Operation	operator: 19 operands: 18
12	Operation	operator: 19 operands: 20
13	Operation	operator: 21 operands: 27
14	Literal
15	ExprTuple	22
16	Literal
17	ExprTuple	30, 23, 24
18	ExprTuple	31, 25
19	Literal
20	ExprTuple	30, 25
21	Literal
22	Operation	operator: 26 operands: 27
23	Operation	operator: 28 operand: 31
24	Literal
25	Literal
26	Literal
27	ExprTuple	31, 30
28	Literal
29	ExprTuple	31
30	Variable
31	Variable