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 And, Equals, InSet
from proveit.numbers import Complex, Exp, Mult, Natural, one

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

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(x, n\right) \mapsto \left\{x^{n} = \left(x \cdot  x \cdot  ..\left(n - 3\right) \times.. \cdot  x\right) \textrm{ if } x \in \mathbb{C} ,  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	parameters: 13 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 11
8	Operation	operator: 12 operands: 13
9	Operation	operator: 14 operands: 15
10	Operation	operator: 17 operands: 16
11	Operation	operator: 17 operands: 18
12	Literal
13	ExprTuple	26, 24
14	Literal
15	ExprTuple	19
16	ExprTuple	26, 20
17	Literal
18	ExprTuple	24, 21
19	ExprRange	lambda_map: 22 start_index: 23 end_index: 24
20	Literal
21	Literal
22	Lambda	parameter: 27 body: 26
23	Literal
24	Variable
25	ExprTuple	27
26	Variable
27	Variable