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Expression of type Lambda

from the theory of proveit.numbers.absolute_value

In [1]:
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
In [2]:
# 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:
In [3]:
# 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
In [4]:
# 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..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameters: 18
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 4
operands: 5
3Operationoperator: 6
operands: 7
4Literal
5ExprTuple8, 9
6Literal
7ExprTuple10
8Operationoperator: 28
operand: 14
9Operationoperator: 17
operands: 12
10ExprRangelambda_map: 13
start_index: 26
end_index: 27
11ExprTuple14
12ExprTuple15
13Lambdaparameter: 33
body: 16
14Operationoperator: 17
operands: 18
15ExprRangelambda_map: 19
start_index: 26
end_index: 27
16Operationoperator: 20
operands: 21
17Literal
18ExprTuple22
19Lambdaparameter: 33
body: 23
20Literal
21ExprTuple30, 24
22ExprRangelambda_map: 25
start_index: 26
end_index: 27
23Operationoperator: 28
operand: 30
24Literal
25Lambdaparameter: 33
body: 30
26Literal
27Variable
28Literal
29ExprTuple30
30IndexedVarvariable: 31
index: 33
31Variable
32ExprTuple33
33Variable