Expression of type Lambda

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, ExprRange, Lambda, Variable, n, x
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Complex, Exp, Mult, NaturalPos, one

# build up the expression from sub-expressions
expr = Lambda(n, Conditional(Forall(instance_param_or_params = [x], instance_expr = Equals(Exp(x, n), Mult(ExprRange(Variable("_a", latex_format = r"{_{-}a}"), x, one, n))), domain = Complex), InSet(n, 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())

n \mapsto \left\{\forall_{x \in \mathbb{C}}~\left(x^{n} = \left(x \cdot  x \cdot  ..\left(n - 3\right) \times.. \cdot  x\right)\right) \textrm{ if } n \in \mathbb{N}^+\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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