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, d
from proveit.logic import And, Equals, InSet, NotEquals
from proveit.numbers import Add, Exp, Integer, Mult, Real, zero

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

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, d\right) \mapsto \left\{a^{b} = \left(a^{c} \cdot a^{d}\right) \textrm{ if } a \in \mathbb{R} ,  b \in \mathbb{Z} ,  c \in \mathbb{Z} ,  d \in \mathbb{Z} ,  a \neq 0 ,  b = \left(c + d\right)\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	40, 33, 41, 42
2	Conditional	value: 3 condition: 4
3	Operation	operator: 26 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 11, 12, 13, 14, 15
8	Operation	operator: 36 operands: 16
9	Operation	operator: 17 operands: 18
10	Operation	operator: 22 operands: 19
11	Operation	operator: 22 operands: 20
12	Operation	operator: 22 operands: 21
13	Operation	operator: 22 operands: 23
14	Operation	operator: 24 operands: 25
15	Operation	operator: 26 operands: 27
16	ExprTuple	40, 33
17	Literal
18	ExprTuple	28, 29
19	ExprTuple	40, 30
20	ExprTuple	33, 31
21	ExprTuple	41, 31
22	Literal
23	ExprTuple	42, 31
24	Literal
25	ExprTuple	40, 32
26	Literal
27	ExprTuple	33, 34
28	Operation	operator: 36 operands: 35
29	Operation	operator: 36 operands: 37
30	Literal
31	Literal
32	Literal
33	Variable
34	Operation	operator: 38 operands: 39
35	ExprTuple	40, 41
36	Literal
37	ExprTuple	40, 42
38	Literal
39	ExprTuple	41, 42
40	Variable
41	Variable
42	Variable