Expression of type Conditional

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, P, Px, n, x
from proveit.core_expr_types import Pk_a1_to_an, a_1_to_n
from proveit.logic import Forall, InSet, Set
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [a_1_to_n], instance_expr = Forall(instance_param_or_params = [P], instance_expr = Forall(instance_param_or_params = [x], instance_expr = Px, domain = Set(a_1_to_n)), condition = Pk_a1_to_an)), 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\{\forall_{a_{1}, a_{2}, \ldots, a_{n}}~\left[\forall_{P~|~P\left(a_{1}\right), P\left(a_{2}\right), \ldots, P\left(a_{n}\right)}~\left[\forall_{x \in \left\{a_{1}, a_{2}, \ldots, a_{n}\right\}}~P\left(x\right)\right]\right] \textrm{ if } n \in \mathbb{N}\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

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