Expression of type ExprTuple

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, ExprTuple, 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 = ExprTuple(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(\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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 26 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12, 13
9	Operation	operator: 25 operands: 14
10	Operation	operator: 25 operands: 15
11	Operation	operator: 17 operands: 16
12	Operation	operator: 17 operands: 18
13	Operation	operator: 19 operands: 20
14	ExprTuple	21, 31
15	ExprTuple	29, 22
16	ExprTuple	29, 23
17	Literal
18	ExprTuple	30, 23
19	Literal
20	ExprTuple	29, 24
21	Operation	operator: 25 operands: 26
22	Operation	operator: 27 operands: 28
23	Literal
24	Literal
25	Literal
26	ExprTuple	29, 30
27	Literal
28	ExprTuple	30, 31
29	Variable
30	Variable
31	Variable