Expression of type Lambda

from the theory of proveit.numbers.integration

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, ExprRange, IndexedVar, Lambda, S, Variable, n, x
from proveit.core_expr_types import f__x_1_to_n, x_1_to_n
from proveit.logic import And, InSet
from proveit.numbers import RealNeg, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda([x_1_to_n], Conditional(InSet(f__x_1_to_n, RealNeg), And(ExprRange(sub_expr1, InSet(IndexedVar(x, sub_expr1), S), one, n))))

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(x_{1}, x_{2}, \ldots, x_{n}\right) \mapsto \left\{f\left(x_{1}, x_{2}, \ldots, x_{n}\right) \in \mathbb{R}^- \textrm{ if } \left(x_{1} \in S\right) \land  \left(x_{2} \in S\right) \land  \ldots \land  \left(x_{n} \in S\right)\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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