logo

Expression of type ExprTuple

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, ExprTuple, Lambda, n, x
from proveit.logic import Equals, InSet
from proveit.numbers import Exp, Mult, Natural, Neg, two
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Mult(two, n)
expr = ExprTuple(Lambda(n, Conditional(Equals(Exp(x, sub_expr1), Exp(Neg(x), sub_expr1)), InSet(n, Natural))))
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(n \mapsto \left\{x^{2 \cdot n} = \left(-x\right)^{2 \cdot n} \textrm{ if } n \in \mathbb{N}\right..\right)
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0ExprTuple1
1Lambdaparameter: 24
body: 3
2ExprTuple24
3Conditionalvalue: 4
condition: 5
4Operationoperator: 6
operands: 7
5Operationoperator: 8
operands: 9
6Literal
7ExprTuple10, 11
8Literal
9ExprTuple24, 12
10Operationoperator: 14
operands: 13
11Operationoperator: 14
operands: 15
12Literal
13ExprTuple22, 17
14Literal
15ExprTuple16, 17
16Operationoperator: 18
operand: 22
17Operationoperator: 20
operands: 21
18Literal
19ExprTuple22
20Literal
21ExprTuple23, 24
22Variable
23Literal
24Variable