Expression of type Conditional

from the theory of proveit.logic.booleans.quantification.existence

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, n
from proveit.logic import Boolean, Forall, InSet
from proveit.logic.booleans.quantification import general_exists_Px
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [P], instance_expr = InSet(general_exists_Px, Boolean)), InSet(n, NaturalPos))

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_{P}~\left(\left[\exists_{x_{1}, x_{2}, \ldots, x_{n}}~P\left(x_{1}, x_{2}, \ldots, x_{n}\right)\right] \in \mathbb{B}\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: 3 operand: 6
2	Operation	operator: 10 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	23, 7
6	Lambda	parameter: 18 body: 9
7	Literal
8	ExprTuple	18
9	Operation	operator: 10 operands: 11
10	Literal
11	ExprTuple	12, 13
12	Operation	operator: 14 operand: 16
13	Literal
14	Literal
15	ExprTuple	16
16	Lambda	parameters: 19 body: 17
17	Operation	operator: 18 operands: 19
18	Variable
19	ExprTuple	20
20	ExprRange	lambda_map: 21 start_index: 22 end_index: 23
21	Lambda	parameter: 27 body: 24
22	Literal
23	Variable
24	IndexedVar	variable: 25 index: 27
25	Variable
26	ExprTuple	27
27	Variable