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Expression of type Lambda

from the theory of proveit.numbers.integration

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, 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 Real, one
In [2]:
# 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, Real), And(ExprRange(sub_expr1, InSet(IndexedVar(x, sub_expr1), S), 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\{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..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameters: 11
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 18
operands: 4
3Operationoperator: 5
operands: 6
4ExprTuple7, 8
5Literal
6ExprTuple9
7Operationoperator: 10
operands: 11
8Literal
9ExprRangelambda_map: 12
start_index: 16
end_index: 17
10Variable
11ExprTuple13
12Lambdaparameter: 24
body: 14
13ExprRangelambda_map: 15
start_index: 16
end_index: 17
14Operationoperator: 18
operands: 19
15Lambdaparameter: 24
body: 20
16Literal
17Variable
18Literal
19ExprTuple20, 21
20IndexedVarvariable: 22
index: 24
21Variable
22Variable
23ExprTuple24
24Variable