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, Forall, InSet, NotInSet
from proveit.numbers import Complex, Integer, Interval

# build up the expression from sub-expressions
expr = Lambda([a, b], Conditional(Forall(instance_param_or_params = [x], instance_expr = NotInSet(x, Interval(a, b)), domain = Complex, condition = NotInSet(x, Integer)), 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 \in \mathbb{C}~|~x \notin \mathbb{Z}}~\left(x \notin \{a~\ldotp \ldotp~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: 23 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operand: 7
3	Operation	operator: 17 operands: 6
4	Literal
5	ExprTuple	7
6	ExprTuple	8, 9
7	Lambda	parameter: 31 body: 11
8	Operation	operator: 24 operands: 12
9	Operation	operator: 24 operands: 13
10	ExprTuple	31
11	Conditional	value: 14 condition: 15
12	ExprTuple	28, 32
13	ExprTuple	29, 32
14	Operation	operator: 26 operands: 16
15	Operation	operator: 17 operands: 18
16	ExprTuple	31, 19
17	Literal
18	ExprTuple	20, 21
19	Operation	operator: 22 operands: 23
20	Operation	operator: 24 operands: 25
21	Operation	operator: 26 operands: 27
22	Literal
23	ExprTuple	28, 29
24	Literal
25	ExprTuple	31, 30
26	Literal
27	ExprTuple	31, 32
28	Variable
29	Variable
30	Literal
31	Variable
32	Literal