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, Equals, 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 = 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())

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