Expression of type Lambda

from the theory of proveit.numbers.absolute_value

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, Variable, n, x
from proveit.core_expr_types import x_1_to_n
from proveit.logic import And, InSet
from proveit.numbers import Abs, Add, Complex, LessEq, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(x, sub_expr1)
expr = Lambda([x_1_to_n], Conditional(LessEq(Abs(Add(x_1_to_n)), Add(ExprRange(sub_expr1, Abs(sub_expr2), one, n))), And(ExprRange(sub_expr1, InSet(sub_expr2, Complex), 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\{\left|x_{1} +  x_{2} +  \ldots +  x_{n}\right| \leq \left(\left|x_{1}\right| +  \left|x_{2}\right| +  \ldots +  \left|x_{n}\right|\right) \textrm{ if } \left(x_{1} \in \mathbb{C}\right) \land  \left(x_{2} \in \mathbb{C}\right) \land  \ldots \land  \left(x_{n} \in \mathbb{C}\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: 18 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10
8	Operation	operator: 28 operand: 14
9	Operation	operator: 17 operands: 12
10	ExprRange	lambda_map: 13 start_index: 26 end_index: 27
11	ExprTuple	14
12	ExprTuple	15
13	Lambda	parameter: 33 body: 16
14	Operation	operator: 17 operands: 18
15	ExprRange	lambda_map: 19 start_index: 26 end_index: 27
16	Operation	operator: 20 operands: 21
17	Literal
18	ExprTuple	22
19	Lambda	parameter: 33 body: 23
20	Literal
21	ExprTuple	30, 24
22	ExprRange	lambda_map: 25 start_index: 26 end_index: 27
23	Operation	operator: 28 operand: 30
24	Literal
25	Lambda	parameter: 33 body: 30
26	Literal
27	Variable
28	Literal
29	ExprTuple	30
30	IndexedVar	variable: 31 index: 33
31	Variable
32	ExprTuple	33
33	Variable