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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 Complex, Exp, Mult, Natural, Neg, two
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Mult(two, n)
expr = Lambda(x, Conditional(Forall(instance_param_or_params = [n], instance_expr = Equals(Exp(x, sub_expr1), Exp(Neg(x), sub_expr1)), domain = Natural), 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\{\forall_{n \in \mathbb{N}}~\left(x^{2 \cdot n} = \left(-x\right)^{2 \cdot n}\right) \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: 29
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 4
operand: 7
3Operationoperator: 15
operands: 6
4Literal
5ExprTuple7
6ExprTuple29, 8
7Lambdaparameter: 31
body: 10
8Literal
9ExprTuple31
10Conditionalvalue: 11
condition: 12
11Operationoperator: 13
operands: 14
12Operationoperator: 15
operands: 16
13Literal
14ExprTuple17, 18
15Literal
16ExprTuple31, 19
17Operationoperator: 21
operands: 20
18Operationoperator: 21
operands: 22
19Literal
20ExprTuple29, 24
21Literal
22ExprTuple23, 24
23Operationoperator: 25
operand: 29
24Operationoperator: 27
operands: 28
25Literal
26ExprTuple29
27Literal
28ExprTuple30, 31
29Variable
30Literal
31Variable