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, InSet
from proveit.numbers import Complex, Exp, Mult, one

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

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())

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

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 21 body: 2
1	ExprTuple	21
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	21, 11
9	Operation	operator: 12 operands: 13
10	Operation	operator: 14 operands: 15
11	Literal
12	Literal
13	ExprTuple	21, 19
14	Literal
15	ExprTuple	16
16	ExprRange	lambda_map: 17 start_index: 18 end_index: 19
17	Lambda	parameter: 22 body: 21
18	Literal
19	Variable
20	ExprTuple	22
21	Variable
22	Variable