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Expression of type Lambda

from the theory of proveit.numbers.exponentiation

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, Lambda, Variable, n, x
from proveit.logic import Equals, InSet
from proveit.numbers import Complex, Exp, Mult, one
In [2]:
# build up the expression from sub-expressions
expr = Lambda(x, Conditional(Equals(Mult(ExprRange(Variable("_a", latex_format = r"{_{-}a}"), x, one, n)), Exp(x, n)), InSet(x, Complex)))
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())
x \mapsto \left\{\left(x \cdot  x \cdot  ..\left(n - 3\right) \times.. \cdot  x\right) = x^{n} \textrm{ if } x \in \mathbb{C}\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameter: 21
body: 2
1ExprTuple21
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operands: 6
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9, 10
7Literal
8ExprTuple21, 11
9Operationoperator: 12
operands: 13
10Operationoperator: 14
operands: 15
11Literal
12Literal
13ExprTuple16
14Literal
15ExprTuple21, 19
16ExprRangelambda_map: 17
start_index: 18
end_index: 19
17Lambdaparameter: 22
body: 21
18Literal
19Variable
20ExprTuple22
21Variable
22Variable