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, c, d
from proveit.logic import And, InSet, ProperSubset
from proveit.numbers import Integer, Interval, Less, LessEq

# build up the expression from sub-expressions
expr = Lambda([a, b, c, d], Conditional(ProperSubset(Interval(b, c), Interval(a, d)), And(InSet(a, Integer), InSet(b, Integer), InSet(c, Integer), InSet(d, Integer), And(Less(a, b), LessEq(b, c), Less(c, d)).with_total_ordering_style())))

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, c, d\right) \mapsto \left\{\{b~\ldotp \ldotp~c\} \subset \{a~\ldotp \ldotp~d\} \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z} ,  c \in \mathbb{Z} ,  d \in \mathbb{Z} ,  a < b \leq c < d\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	33, 34, 35, 36
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 22 operands: 7
5	Literal
6	ExprTuple	8, 9
7	ExprTuple	10, 11, 12, 13, 14
8	Operation	operator: 15 operands: 30
9	Operation	operator: 15 operands: 16
10	Operation	operator: 20 operands: 17
11	Operation	operator: 20 operands: 18
12	Operation	operator: 20 operands: 19
13	Operation	operator: 20 operands: 21
14	Operation	operator: 22 operands: 23
15	Literal
16	ExprTuple	33, 36
17	ExprTuple	33, 24
18	ExprTuple	34, 24
19	ExprTuple	35, 24
20	Literal
21	ExprTuple	36, 24
22	Literal
23	ExprTuple	25, 26, 27
24	Literal
25	Operation	operator: 31 operands: 28
26	Operation	operator: 29 operands: 30
27	Operation	operator: 31 operands: 32
28	ExprTuple	33, 34
29	Literal
30	ExprTuple	34, 35
31	Literal
32	ExprTuple	35, 36
33	Variable
34	Variable
35	Variable
36	Variable