Expression of type Lambda

from the theory of proveit.logic.sets.enumeration

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, P, Px, n, x
from proveit.core_expr_types import Pk_a1_to_an, a_1_to_n
from proveit.logic import And, Forall, InSet, Set
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = Lambda(n, Conditional(Forall(instance_param_or_params = [a_1_to_n], instance_expr = Forall(instance_param_or_params = [P], instance_expr = And(Pk_a1_to_an), condition = Forall(instance_param_or_params = [x], instance_expr = Px, domain = Set(a_1_to_n)))), InSet(n, Natural)))

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())

n \mapsto \left\{\forall_{a_{1}, a_{2}, \ldots, a_{n}}~\left[\forall_{P~|~\forall_{x \in \left\{a_{1}, a_{2}, \ldots, a_{n}\right\}}~P\left(x\right)}~\left(P\left(a_{1}\right) \land  P\left(a_{2}\right) \land  \ldots \land  P\left(a_{n}\right)\right)\right] \textrm{ if } 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	parameter: 39 body: 2
1	ExprTuple	39
2	Conditional	value: 3 condition: 4
3	Operation	operator: 18 operand: 7
4	Operation	operator: 30 operands: 6
5	ExprTuple	7
6	ExprTuple	39, 8
7	Lambda	parameters: 35 body: 9
8	Literal
9	Operation	operator: 18 operand: 11
10	ExprTuple	11
11	Lambda	parameter: 28 body: 13
12	ExprTuple	28
13	Conditional	value: 14 condition: 15
14	Operation	operator: 16 operands: 17
15	Operation	operator: 18 operand: 21
16	Literal
17	ExprTuple	20
18	Literal
19	ExprTuple	21
20	ExprRange	lambda_map: 22 start_index: 38 end_index: 39
21	Lambda	parameter: 32 body: 23
22	Lambda	parameter: 43 body: 24
23	Conditional	value: 25 condition: 26
24	Operation	operator: 28 operand: 40
25	Operation	operator: 28 operand: 32
26	Operation	operator: 30 operands: 31
27	ExprTuple	40
28	Variable
29	ExprTuple	32
30	Literal
31	ExprTuple	32, 33
32	Variable
33	Operation	operator: 34 operands: 35
34	Literal
35	ExprTuple	36
36	ExprRange	lambda_map: 37 start_index: 38 end_index: 39
37	Lambda	parameter: 43 body: 40
38	Literal
39	Variable
40	IndexedVar	variable: 41 index: 43
41	Variable
42	ExprTuple	43
43	Variable