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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, Lambda, n, x
from proveit.logic import Equals
from proveit.numbers import Exp, frac, greater_eq, one, zero
In [2]:
# build up the expression from sub-expressions
expr = Lambda(x, Conditional(Equals(Exp(Exp(x, n), frac(one, n)), x), greater_eq(x, zero)))
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\{\sqrt[\leftroot{-3}\uproot{3}n]{(x^{n})} = x \textrm{ if } x \geq 0\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameter: 18
body: 2
1ExprTuple18
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operands: 6
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9, 18
7Literal
8ExprTuple10, 18
9Operationoperator: 14
operands: 11
10Literal
11ExprTuple12, 13
12Operationoperator: 14
operands: 15
13Operationoperator: 16
operands: 17
14Literal
15ExprTuple18, 20
16Literal
17ExprTuple19, 20
18Variable
19Literal
20Variable