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, a, b, c
from proveit.logic import And, Equals, InSet
from proveit.numbers import Complex, Exp, Mult, RealPos
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda([a, b, c], Conditional(Equals(Exp(Exp(a, b), c), Exp(a, Mult(b, c))), And(InSet(a, Complex), InSet(b, RealPos), InSet(c, RealPos)))))
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(\left(a, b, c\right) \mapsto \left\{(a^{b})^{c} = a^{b \cdot c} \textrm{ if } a \in \mathbb{C} ,  b \in \mathbb{R}^+ ,  c \in \mathbb{R}^+\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
1Lambdaparameters: 2
body: 3
2ExprTuple29, 30, 31
3Conditionalvalue: 4
condition: 5
4Operationoperator: 6
operands: 7
5Operationoperator: 8
operands: 9
6Literal
7ExprTuple10, 11
8Literal
9ExprTuple12, 13, 14
10Operationoperator: 25
operands: 15
11Operationoperator: 25
operands: 16
12Operationoperator: 19
operands: 17
13Operationoperator: 19
operands: 18
14Operationoperator: 19
operands: 20
15ExprTuple21, 31
16ExprTuple29, 22
17ExprTuple29, 23
18ExprTuple30, 24
19Literal
20ExprTuple31, 24
21Operationoperator: 25
operands: 26
22Operationoperator: 27
operands: 28
23Literal
24Literal
25Literal
26ExprTuple29, 30
27Literal
28ExprTuple30, 31
29Variable
30Variable
31Variable