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 Lambda, P, Py, S, y, z
from proveit.logic import Equals, Forall, Implies, InSet, NotEquals
from proveit.numbers import Complex, Sum, frac, zero

# build up the expression from sub-expressions
sub_expr1 = [y]
expr = Lambda([P, S], Implies(Forall(instance_param_or_params = sub_expr1, instance_expr = InSet(Py, Complex), domain = S), Forall(instance_param_or_params = [z], instance_expr = 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)), domain = Complex, condition = 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())

\left(P, S\right) \mapsto \left(\left[\forall_{y \in S}~\left(P\left(y\right) \in \mathbb{C}\right)\right] \Rightarrow \left[\forall_{z \in \mathbb{C}~|~z \neq 0}~\left(\frac{\sum_{y \in S}~P\left(y\right)}{z} = \left[\sum_{y \in S}~\frac{P\left(y\right)}{z}\right]\right)\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	49, 51
2	Operation	operator: 3 operands: 4
3	Literal
4	ExprTuple	5, 6
5	Operation	operator: 8 operand: 10
6	Operation	operator: 8 operand: 11
7	ExprTuple	10
8	Literal
9	ExprTuple	11
10	Lambda	parameter: 52 body: 12
11	Lambda	parameter: 46 body: 14
12	Conditional	value: 15 condition: 44
13	ExprTuple	46
14	Conditional	value: 16 condition: 17
15	Operation	operator: 47 operands: 18
16	Operation	operator: 19 operands: 20
17	Operation	operator: 21 operands: 22
18	ExprTuple	45, 34
19	Literal
20	ExprTuple	23, 24
21	Literal
22	ExprTuple	25, 26
23	Operation	operator: 42 operands: 27
24	Operation	operator: 36 operand: 33
25	Operation	operator: 47 operands: 29
26	Operation	operator: 30 operands: 31
27	ExprTuple	32, 46
28	ExprTuple	33
29	ExprTuple	46, 34
30	Literal
31	ExprTuple	46, 35
32	Operation	operator: 36 operand: 39
33	Lambda	parameter: 52 body: 38
34	Literal
35	Literal
36	Literal
37	ExprTuple	39
38	Conditional	value: 40 condition: 44
39	Lambda	parameter: 52 body: 41
40	Operation	operator: 42 operands: 43
41	Conditional	value: 45 condition: 44
42	Literal
43	ExprTuple	45, 46
44	Operation	operator: 47 operands: 48
45	Operation	operator: 49 operand: 52
46	Variable
47	Literal
48	ExprTuple	52, 51
49	Variable
50	ExprTuple	52
51	Variable
52	Variable