Expression of type Lambda

from the theory of proveit.numbers.multiplication

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, k
from proveit.logic import And, Equals, InSet, NotEquals
from proveit.numbers import Complex, Exp, Mult, zero

# build up the expression from sub-expressions
expr = Lambda([a, b], Conditional(Equals(Exp(Exp(a, b), k), Exp(a, Mult(b, k))), And(InSet(a, Complex), InSet(b, Complex), NotEquals(a, zero))))

expr:

# 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

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(a, b\right) \mapsto \left\{(a^{b})^{k} = a^{b \cdot k} \textrm{ if } a \in \mathbb{C} ,  b \in \mathbb{C} ,  a \neq 0\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 25 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 11, 12
8	Operation	operator: 24 operands: 13
9	Operation	operator: 24 operands: 14
10	Operation	operator: 16 operands: 15
11	Operation	operator: 16 operands: 17
12	Operation	operator: 18 operands: 19
13	ExprTuple	20, 30
14	ExprTuple	28, 21
15	ExprTuple	28, 22
16	Literal
17	ExprTuple	29, 22
18	Literal
19	ExprTuple	28, 23
20	Operation	operator: 24 operands: 25
21	Operation	operator: 26 operands: 27
22	Literal
23	Literal
24	Literal
25	ExprTuple	28, 29
26	Literal
27	ExprTuple	29, 30
28	Variable
29	Variable
30	Variable