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, ExprRange, Function, IndexedVar, Lambda, P, Px, Variable, a, n, x
from proveit.core_expr_types import a_1_to_n
from proveit.logic import Equals, FALSE, Forall, InSet, Or, Set
from proveit.numbers import Natural, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda(n, Conditional(Forall(instance_param_or_params = [a_1_to_n], instance_expr = Forall(instance_param_or_params = [P], instance_expr = Equals(Or(ExprRange(sub_expr1, Equals(Function(P, [IndexedVar(a, sub_expr1)]), FALSE), one, n)), Equals(Forall(instance_param_or_params = [x], instance_expr = Px, domain = Set(a_1_to_n)), FALSE)))), 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(\left(P\left(a_{1}\right) = \bot\right) \lor  \left(P\left(a_{2}\right) = \bot\right) \lor  \ldots \lor  \left(P\left(a_{n}\right) = \bot\right)\right) = \left(\left[\forall_{x \in \left\{a_{1}, a_{2}, \ldots, a_{n}\right\}}~P\left(x\right)\right] = \bot\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: 46 body: 2
1	ExprTuple	46
2	Conditional	value: 3 condition: 4
3	Operation	operator: 23 operand: 7
4	Operation	operator: 37 operands: 6
5	ExprTuple	7
6	ExprTuple	46, 8
7	Lambda	parameters: 42 body: 9
8	Literal
9	Operation	operator: 23 operand: 11
10	ExprTuple	11
11	Lambda	parameter: 35 body: 13
12	ExprTuple	35
13	Operation	operator: 27 operands: 14
14	ExprTuple	15, 16
15	Operation	operator: 17 operands: 18
16	Operation	operator: 27 operands: 19
17	Literal
18	ExprTuple	20
19	ExprTuple	21, 31
20	ExprRange	lambda_map: 22 start_index: 45 end_index: 46
21	Operation	operator: 23 operand: 26
22	Lambda	parameter: 50 body: 25
23	Literal
24	ExprTuple	26
25	Operation	operator: 27 operands: 28
26	Lambda	parameter: 39 body: 29
27	Literal
28	ExprTuple	30, 31
29	Conditional	value: 32 condition: 33
30	Operation	operator: 35 operand: 47
31	Literal
32	Operation	operator: 35 operand: 39
33	Operation	operator: 37 operands: 38
34	ExprTuple	47
35	Variable
36	ExprTuple	39
37	Literal
38	ExprTuple	39, 40
39	Variable
40	Operation	operator: 41 operands: 42
41	Literal
42	ExprTuple	43
43	ExprRange	lambda_map: 44 start_index: 45 end_index: 46
44	Lambda	parameter: 50 body: 47
45	Literal
46	Variable
47	IndexedVar	variable: 48 index: 50
48	Variable
49	ExprTuple	50
50	Variable