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, b, c
from proveit.logic import And, Equals, InSet, NotEquals
from proveit.numbers import Complex, Exp, Mult, Neg, Real, zero

# build up the expression from sub-expressions
expr = Lambda([a, b, c], Conditional(Equals(Exp(Exp(a, b), Neg(c)), Exp(a, Neg(Mult(b, c)))), And(InSet(a, Complex), InSet(b, Real), InSet(c, Real), NotEquals(a, zero))))

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, b, c\right) \mapsto \left\{(a^{b})^{-c} = a^{-\left(b \cdot c\right)} \textrm{ if } a \in \mathbb{C} ,  b \in \mathbb{R} ,  c \in \mathbb{R} ,  a \neq 0\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	34, 38, 39
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	11, 12, 13, 14
9	Operation	operator: 29 operands: 15
10	Operation	operator: 29 operands: 16
11	Operation	operator: 19 operands: 17
12	Operation	operator: 19 operands: 18
13	Operation	operator: 19 operands: 20
14	Operation	operator: 21 operands: 22
15	ExprTuple	23, 24
16	ExprTuple	34, 25
17	ExprTuple	34, 26
18	ExprTuple	38, 27
19	Literal
20	ExprTuple	39, 27
21	Literal
22	ExprTuple	34, 28
23	Operation	operator: 29 operands: 30
24	Operation	operator: 32 operand: 39
25	Operation	operator: 32 operand: 35
26	Literal
27	Literal
28	Literal
29	Literal
30	ExprTuple	34, 38
31	ExprTuple	39
32	Literal
33	ExprTuple	35
34	Variable
35	Operation	operator: 36 operands: 37
36	Literal
37	ExprTuple	38, 39
38	Variable
39	Variable