Expression of type Lambda

from the theory of proveit.numbers.division

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, Py, S, y, z
from proveit.logic import And, Equals, InSet, NotEquals
from proveit.numbers import Complex, Sum, frac, zero

# build up the expression from sub-expressions
sub_expr1 = [y]
expr = Lambda(z, Conditional(Equals(frac(Sum(index_or_indices = sub_expr1, summand = Py, domain = S), z), Sum(index_or_indices = sub_expr1, summand = frac(Py, z), domain = S)), And(InSet(z, Complex), NotEquals(z, 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())

z \mapsto \left\{\frac{\sum_{y \in S}~P\left(y\right)}{z} = \left[\sum_{y \in S}~\frac{P\left(y\right)}{z}\right] \textrm{ if } z \in \mathbb{C} ,  z \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	parameter: 32 body: 2
1	ExprTuple	32
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
9	Operation	operator: 28 operands: 13
10	Operation	operator: 22 operand: 19
11	Operation	operator: 33 operands: 15
12	Operation	operator: 16 operands: 17
13	ExprTuple	18, 32
14	ExprTuple	19
15	ExprTuple	32, 20
16	Literal
17	ExprTuple	32, 21
18	Operation	operator: 22 operand: 25
19	Lambda	parameter: 38 body: 24
20	Literal
21	Literal
22	Literal
23	ExprTuple	25
24	Conditional	value: 26 condition: 30
25	Lambda	parameter: 38 body: 27
26	Operation	operator: 28 operands: 29
27	Conditional	value: 31 condition: 30
28	Literal
29	ExprTuple	31, 32
30	Operation	operator: 33 operands: 34
31	Operation	operator: 35 operand: 38
32	Variable
33	Literal
34	ExprTuple	38, 37
35	Variable
36	ExprTuple	38
37	Variable
38	Variable