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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, Forall, InSet
from proveit.numbers import Exp, NaturalPos, frac, greater_eq, one, zero
In [2]:
# build up the expression from sub-expressions
expr = Lambda(n, Conditional(Forall(instance_param_or_params = [x], instance_expr = Equals(Exp(Exp(x, frac(one, n)), n), x), condition = greater_eq(x, zero)), InSet(n, NaturalPos)))
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())
n \mapsto \left\{\forall_{x~|~x \geq 0}~\left((\sqrt[\leftroot{-3}\uproot{3}n]{x})^{n} = x\right) \textrm{ if } n \in \mathbb{N}^+\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameter: 30
body: 2
1ExprTuple30
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operand: 9
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9
7Literal
8ExprTuple30, 10
9Lambdaparameter: 25
body: 12
10Literal
11ExprTuple25
12Conditionalvalue: 13
condition: 14
13Operationoperator: 15
operands: 16
14Operationoperator: 17
operands: 18
15Literal
16ExprTuple19, 25
17Literal
18ExprTuple20, 25
19Operationoperator: 23
operands: 21
20Literal
21ExprTuple22, 30
22Operationoperator: 23
operands: 24
23Literal
24ExprTuple25, 26
25Variable
26Operationoperator: 27
operands: 28
27Literal
28ExprTuple29, 30
29Literal
30Variable