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, Equals, 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 = Equals(And(Pk_a1_to_an), 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}~\left(\left(P\left(a_{1}\right) \land  P\left(a_{2}\right) \land  \ldots \land  P\left(a_{n}\right)\right) = \left[\forall_{x \in \left\{a_{1}, a_{2}, \ldots, a_{n}\right\}}~P\left(x\right)\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: 41 body: 2
1	ExprTuple	41
2	Conditional	value: 3 condition: 4
3	Operation	operator: 20 operand: 7
4	Operation	operator: 32 operands: 6
5	ExprTuple	7
6	ExprTuple	41, 8
7	Lambda	parameters: 37 body: 9
8	Literal
9	Operation	operator: 20 operand: 11
10	ExprTuple	11
11	Lambda	parameter: 30 body: 13
12	ExprTuple	30
13	Operation	operator: 14 operands: 15
14	Literal
15	ExprTuple	16, 17
16	Operation	operator: 18 operands: 19
17	Operation	operator: 20 operand: 23
18	Literal
19	ExprTuple	22
20	Literal
21	ExprTuple	23
22	ExprRange	lambda_map: 24 start_index: 40 end_index: 41
23	Lambda	parameter: 34 body: 25
24	Lambda	parameter: 45 body: 26
25	Conditional	value: 27 condition: 28
26	Operation	operator: 30 operand: 42
27	Operation	operator: 30 operand: 34
28	Operation	operator: 32 operands: 33
29	ExprTuple	42
30	Variable
31	ExprTuple	34
32	Literal
33	ExprTuple	34, 35
34	Variable
35	Operation	operator: 36 operands: 37
36	Literal
37	ExprTuple	38
38	ExprRange	lambda_map: 39 start_index: 40 end_index: 41
39	Lambda	parameter: 45 body: 42
40	Literal
41	Variable
42	IndexedVar	variable: 43 index: 45
43	Variable
44	ExprTuple	45
45	Variable