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
from proveit.numbers import Add, Exp, Mult, Real, RealPos

# 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, RealPos), InSet(b, Real), InSet(c, Real), InSet(d, Real), 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{R} ,  c \in \mathbb{R} ,  d \in \mathbb{R} ,  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	37, 30, 38, 39
3	Conditional	value: 4 condition: 5
4	Operation	operator: 24 operands: 6
5	Operation	operator: 7 operands: 8
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12, 13, 14, 15
9	Operation	operator: 33 operands: 16
10	Operation	operator: 17 operands: 18
11	Operation	operator: 22 operands: 19
12	Operation	operator: 22 operands: 20
13	Operation	operator: 22 operands: 21
14	Operation	operator: 22 operands: 23
15	Operation	operator: 24 operands: 25
16	ExprTuple	37, 30
17	Literal
18	ExprTuple	26, 27
19	ExprTuple	37, 28
20	ExprTuple	30, 29
21	ExprTuple	38, 29
22	Literal
23	ExprTuple	39, 29
24	Literal
25	ExprTuple	30, 31
26	Operation	operator: 33 operands: 32
27	Operation	operator: 33 operands: 34
28	Literal
29	Literal
30	Variable
31	Operation	operator: 35 operands: 36
32	ExprTuple	37, 38
33	Literal
34	ExprTuple	37, 39
35	Literal
36	ExprTuple	38, 39
37	Variable
38	Variable
39	Variable