Expression of type ExprTuple

from the theory of proveit.numbers.exponentiation

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, d
from proveit.logic import And, Equals, InSet, NotEquals
from proveit.numbers import Add, Exp, Integer, Mult, Real, zero

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([a, b, c, d], Conditional(Equals(Exp(a, b), Mult(Exp(a, c), Exp(a, d))), And(InSet(a, Real), InSet(b, Integer), InSet(c, Integer), InSet(d, Integer), NotEquals(a, zero), Equals(b, Add(c, d))))))

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, c, d\right) \mapsto \left\{a^{b} = \left(a^{c} \cdot a^{d}\right) \textrm{ if } a \in \mathbb{R} ,  b \in \mathbb{Z} ,  c \in \mathbb{Z} ,  d \in \mathbb{Z} ,  a \neq 0 ,  b = \left(c + d\right)\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: 2 body: 3
2	ExprTuple	41, 34, 42, 43
3	Conditional	value: 4 condition: 5
4	Operation	operator: 27 operands: 6
5	Operation	operator: 7 operands: 8
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12, 13, 14, 15, 16
9	Operation	operator: 37 operands: 17
10	Operation	operator: 18 operands: 19
11	Operation	operator: 23 operands: 20
12	Operation	operator: 23 operands: 21
13	Operation	operator: 23 operands: 22
14	Operation	operator: 23 operands: 24
15	Operation	operator: 25 operands: 26
16	Operation	operator: 27 operands: 28
17	ExprTuple	41, 34
18	Literal
19	ExprTuple	29, 30
20	ExprTuple	41, 31
21	ExprTuple	34, 32
22	ExprTuple	42, 32
23	Literal
24	ExprTuple	43, 32
25	Literal
26	ExprTuple	41, 33
27	Literal
28	ExprTuple	34, 35
29	Operation	operator: 37 operands: 36
30	Operation	operator: 37 operands: 38
31	Literal
32	Literal
33	Literal
34	Variable
35	Operation	operator: 39 operands: 40
36	ExprTuple	41, 42
37	Literal
38	ExprTuple	41, 43
39	Literal
40	ExprTuple	42, 43
41	Variable
42	Variable
43	Variable