Expression of type Lambda

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, Lambda, a, b, x
from proveit.logic import And, InSet, NotInSet, Or
from proveit.numbers import Integer, Interval, Less

# build up the expression from sub-expressions
expr = Lambda([a, b, x], Conditional(NotInSet(x, Interval(a, b)), And(InSet(a, Integer), InSet(b, Integer), InSet(x, Integer), Or(Less(x, a), Less(b, x)))))

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, b, x\right) \mapsto \left\{x \notin \{a~\ldotp \ldotp~b\} \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z} ,  x \in \mathbb{Z} ,  \left(x < a\right) \lor \left(b < x\right)\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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