Expression of type ExprTuple

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, ExprTuple, 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 = ExprTuple(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())

\left(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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 47 body: 3
2	ExprTuple	47
3	Conditional	value: 4 condition: 5
4	Operation	operator: 24 operand: 8
5	Operation	operator: 38 operands: 7
6	ExprTuple	8
7	ExprTuple	47, 9
8	Lambda	parameters: 43 body: 10
9	Literal
10	Operation	operator: 24 operand: 12
11	ExprTuple	12
12	Lambda	parameter: 36 body: 14
13	ExprTuple	36
14	Operation	operator: 28 operands: 15
15	ExprTuple	16, 17
16	Operation	operator: 18 operands: 19
17	Operation	operator: 28 operands: 20
18	Literal
19	ExprTuple	21
20	ExprTuple	22, 32
21	ExprRange	lambda_map: 23 start_index: 46 end_index: 47
22	Operation	operator: 24 operand: 27
23	Lambda	parameter: 51 body: 26
24	Literal
25	ExprTuple	27
26	Operation	operator: 28 operands: 29
27	Lambda	parameter: 40 body: 30
28	Literal
29	ExprTuple	31, 32
30	Conditional	value: 33 condition: 34
31	Operation	operator: 36 operand: 48
32	Literal
33	Operation	operator: 36 operand: 40
34	Operation	operator: 38 operands: 39
35	ExprTuple	48
36	Variable
37	ExprTuple	40
38	Literal
39	ExprTuple	40, 41
40	Variable
41	Operation	operator: 42 operands: 43
42	Literal
43	ExprTuple	44
44	ExprRange	lambda_map: 45 start_index: 46 end_index: 47
45	Lambda	parameter: 51 body: 48
46	Literal
47	Variable
48	IndexedVar	variable: 49 index: 51
49	Variable
50	ExprTuple	51
51	Variable