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, ExprTuple, 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 = ExprTuple(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())

\left(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..\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: 40 body: 3
2	ExprTuple	40
3	Conditional	value: 4 condition: 5
4	Operation	operator: 19 operand: 8
5	Operation	operator: 31 operands: 7
6	ExprTuple	8
7	ExprTuple	40, 9
8	Lambda	parameters: 36 body: 10
9	Literal
10	Operation	operator: 19 operand: 12
11	ExprTuple	12
12	Lambda	parameter: 29 body: 14
13	ExprTuple	29
14	Conditional	value: 15 condition: 16
15	Operation	operator: 17 operands: 18
16	Operation	operator: 19 operand: 22
17	Literal
18	ExprTuple	21
19	Literal
20	ExprTuple	22
21	ExprRange	lambda_map: 23 start_index: 39 end_index: 40
22	Lambda	parameter: 33 body: 24
23	Lambda	parameter: 44 body: 25
24	Conditional	value: 26 condition: 27
25	Operation	operator: 29 operand: 41
26	Operation	operator: 29 operand: 33
27	Operation	operator: 31 operands: 32
28	ExprTuple	41
29	Variable
30	ExprTuple	33
31	Literal
32	ExprTuple	33, 34
33	Variable
34	Operation	operator: 35 operands: 36
35	Literal
36	ExprTuple	37
37	ExprRange	lambda_map: 38 start_index: 39 end_index: 40
38	Lambda	parameter: 44 body: 41
39	Literal
40	Variable
41	IndexedVar	variable: 42 index: 44
42	Variable
43	ExprTuple	44
44	Variable