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, Px, x
from proveit.core_expr_types import Pk_a1_to_an, a_1_to_n
from proveit.logic import And, Forall, Set

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [x], instance_expr = Px, domain = Set(a_1_to_n)), And(Pk_a1_to_an))

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_{x \in \left\{a_{1}, a_{2}, \ldots, a_{n}\right\}}~P\left(x\right) \textrm{ if } P\left(a_{1}\right) \land  P\left(a_{2}\right) \land  \ldots \land  P\left(a_{n}\right)\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: 3 operand: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	8
7	Lambda	parameter: 19 body: 9
8	ExprRange	lambda_map: 10 start_index: 25 end_index: 26
9	Conditional	value: 11 condition: 12
10	Lambda	parameter: 30 body: 13
11	Operation	operator: 17 operand: 19
12	Operation	operator: 15 operands: 16
13	Operation	operator: 17 operand: 27
14	ExprTuple	19
15	Literal
16	ExprTuple	19, 20
17	Variable
18	ExprTuple	27
19	Variable
20	Operation	operator: 21 operands: 22
21	Literal
22	ExprTuple	23
23	ExprRange	lambda_map: 24 start_index: 25 end_index: 26
24	Lambda	parameter: 30 body: 27
25	Literal
26	Variable
27	IndexedVar	variable: 28 index: 30
28	Variable
29	ExprTuple	30
30	Variable