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

# build up the expression from sub-expressions
expr = Lambda([a, b], Conditional(Forall(instance_param_or_params = [x], instance_expr = Equals(InSet(x, IntervalOO(a, b)), And(InSet(x, Real), And(Less(a, x), Less(x, b)).with_total_ordering_style()))), And(InSet(a, Real), InSet(b, Real))))

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 \left(a,b\right)\right) = \left(\left(x \in \mathbb{R}\right) \land \left(a < x < b\right)\right)\right) \textrm{ if } a \in \mathbb{R} ,  b \in \mathbb{R}\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: 7
3	Operation	operator: 27 operands: 6
4	Literal
5	ExprTuple	7
6	ExprTuple	8, 9
7	Lambda	parameter: 36 body: 11
8	Operation	operator: 25 operands: 12
9	Operation	operator: 25 operands: 13
10	ExprTuple	36
11	Operation	operator: 14 operands: 15
12	ExprTuple	35, 29
13	ExprTuple	37, 29
14	Literal
15	ExprTuple	16, 17
16	Operation	operator: 25 operands: 18
17	Operation	operator: 27 operands: 19
18	ExprTuple	36, 20
19	ExprTuple	21, 22
20	Operation	operator: 23 operands: 24
21	Operation	operator: 25 operands: 26
22	Operation	operator: 27 operands: 28
23	Literal
24	ExprTuple	35, 37
25	Literal
26	ExprTuple	36, 29
27	Literal
28	ExprTuple	30, 31
29	Literal
30	Operation	operator: 33 operands: 32
31	Operation	operator: 33 operands: 34
32	ExprTuple	35, 36
33	Literal
34	ExprTuple	36, 37
35	Variable
36	Variable
37	Variable