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, Lambda, a, n
from proveit.logic import And, Equals, InSet
from proveit.numbers import ComplexNonZero, Exp, NaturalPos, Neg, frac, one

# build up the expression from sub-expressions
expr = Lambda([a, n], Conditional(Equals(Exp(a, Neg(n)), frac(one, Exp(a, n))), And(InSet(a, ComplexNonZero), 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())

\left(a, n\right) \mapsto \left\{a^{-n} = \frac{1}{a^{n}} \textrm{ if } a \in \mathbb{C}^{\neq 0} ,  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: 26 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: 25 operands: 12
9	Operation	operator: 13 operands: 14
10	Operation	operator: 16 operands: 15
11	Operation	operator: 16 operands: 17
12	ExprTuple	27, 18
13	Literal
14	ExprTuple	19, 20
15	ExprTuple	27, 21
16	Literal
17	ExprTuple	28, 22
18	Operation	operator: 23 operand: 28
19	Literal
20	Operation	operator: 25 operands: 26
21	Literal
22	Literal
23	Literal
24	ExprTuple	28
25	Literal
26	ExprTuple	27, 28
27	Variable
28	Variable