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, Boolean, Forall, InSet
from proveit.numbers import Integer, Interval

# build up the expression from sub-expressions
expr = Lambda([a, b], Conditional(Forall(instance_param_or_params = [x], instance_expr = InSet(InSet(x, Interval(a, b)), Boolean)), And(InSet(a, Integer), InSet(b, Integer))))

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

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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