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, m
from proveit.core_expr_types import b_1_to_m
from proveit.logic import Equals, Forall, InSet, NotEquals
from proveit.numbers import Add, Complex, Exp, NaturalPos, Real, zero
from proveit.numbers.exponentiation import prod_a_raise_bi__1_to_m

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(m, Conditional(Forall(instance_param_or_params = [a, b_1_to_m], instance_expr = Equals(prod_a_raise_bi__1_to_m, Exp(a, Add(b_1_to_m))), domains = [Complex, Real], condition = NotEquals(a, zero)), InSet(m, NaturalPos))))

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(m \mapsto \left\{\forall_{a \in \mathbb{C},\left(b_{1} \in \mathbb{R}\right), \left(b_{2} \in \mathbb{R}\right), \ldots, \left(b_{m} \in \mathbb{R}\right)~|~a \neq 0}~\left(\left(a^{b_{1}} \cdot  a^{b_{2}} \cdot  \ldots \cdot  a^{b_{m}}\right) = a^{b_{1} +  b_{2} +  \ldots +  b_{m}}\right) \textrm{ if } m \in \mathbb{N}^+\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	parameter: 48 body: 3
2	ExprTuple	48
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 39 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	48, 10
9	Lambda	parameters: 11 body: 12
10	Literal
11	ExprTuple	49, 42
12	Conditional	value: 13 condition: 14
13	Operation	operator: 15 operands: 16
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	21, 22, 23
19	Operation	operator: 24 operands: 25
20	Operation	operator: 44 operands: 26
21	Operation	operator: 39 operands: 27
22	ExprRange	lambda_map: 28 start_index: 47 end_index: 48
23	Operation	operator: 29 operands: 30
24	Literal
25	ExprTuple	31
26	ExprTuple	49, 32
27	ExprTuple	49, 33
28	Lambda	parameter: 53 body: 34
29	Literal
30	ExprTuple	49, 35
31	ExprRange	lambda_map: 36 start_index: 47 end_index: 48
32	Operation	operator: 37 operands: 38
33	Literal
34	Operation	operator: 39 operands: 40
35	Literal
36	Lambda	parameter: 53 body: 41
37	Literal
38	ExprTuple	42
39	Literal
40	ExprTuple	50, 43
41	Operation	operator: 44 operands: 45
42	ExprRange	lambda_map: 46 start_index: 47 end_index: 48
43	Literal
44	Literal
45	ExprTuple	49, 50
46	Lambda	parameter: 53 body: 50
47	Literal
48	Variable
49	Variable
50	IndexedVar	variable: 51 index: 53
51	Variable
52	ExprTuple	53
53	Variable