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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, a, b, c
from proveit.logic import And, Equals, InSet, NotEquals
from proveit.numbers import Complex, Exp, Mult, Real, zero
In [2]:
# build up the expression from sub-expressions
expr = Lambda([a, b, c], Conditional(Equals(Exp(Exp(a, b), c), Exp(a, Mult(b, c))), And(InSet(a, Complex), InSet(b, Real), InSet(c, Real), NotEquals(a, 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())
\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} ,  a \neq 0\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameters: 1
body: 2
1ExprTuple32, 33, 34
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operands: 6
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9, 10
7Literal
8ExprTuple11, 12, 13, 14
9Operationoperator: 28
operands: 15
10Operationoperator: 28
operands: 16
11Operationoperator: 19
operands: 17
12Operationoperator: 19
operands: 18
13Operationoperator: 19
operands: 20
14Operationoperator: 21
operands: 22
15ExprTuple23, 34
16ExprTuple32, 24
17ExprTuple32, 25
18ExprTuple33, 26
19Literal
20ExprTuple34, 26
21Literal
22ExprTuple32, 27
23Operationoperator: 28
operands: 29
24Operationoperator: 30
operands: 31
25Literal
26Literal
27Literal
28Literal
29ExprTuple32, 33
30Literal
31ExprTuple33, 34
32Variable
33Variable
34Variable