Expression of type Lambda

from the theory of proveit.numbers.number_sets.real_numbers

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 Lambda, a, b, x
from proveit.logic import And, Equals, InSet
from proveit.numbers import IntervalOO, Less, Real

# build up the expression from sub-expressions
expr = Lambda(x, Equals(InSet(x, IntervalOO(a, b)), And(InSet(x, Real), And(Less(a, x), Less(x, b)).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())

x \mapsto \left(\left(x \in \left(a,b\right)\right) = \left(\left(x \in \mathbb{R}\right) \land \left(a < x < b\right)\right)\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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