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, n
from proveit.logic import And, Forall, InSet
from proveit.numbers import Integer, Interval, LessEq

# build up the expression from sub-expressions
expr = Lambda([a, b], Conditional(Forall(instance_param_or_params = [n], instance_expr = LessEq(n, b), domain = Interval(a, b)), 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_{n \in \{a~\ldotp \ldotp~b\}}~\left(n \leq 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: 25 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: 22 body: 12
9	Operation	operator: 20 operands: 13
10	Operation	operator: 20 operands: 14
11	ExprTuple	22
12	Conditional	value: 15 condition: 16
13	ExprTuple	26, 17
14	ExprTuple	27, 17
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operands: 21
17	Literal
18	Literal
19	ExprTuple	22, 27
20	Literal
21	ExprTuple	22, 23
22	Variable
23	Operation	operator: 24 operands: 25
24	Literal
25	ExprTuple	26, 27
26	Variable
27	Variable