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, Q, n
from proveit.logic import Forall, InSet, Not
from proveit.logic.booleans.quantification import general_exists_Px_st_Qx, general_forall__Py_not_T__st_Qy
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [P, Q], instance_expr = general_exists_Px_st_Qx, condition = Not(general_forall__Py_not_T__st_Qy)), 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, Q~|~\lnot \left[\forall_{y_{1}, y_{2}, \ldots, y_{n}~|~Q\left(y_{1}, y_{2}, \ldots, y_{n}\right)}~\left(P\left(y_{1}, y_{2}, \ldots, y_{n}\right) \neq \top\right)\right]}~\left[\exists_{x_{1}, x_{2}, \ldots, x_{n}~|~Q\left(x_{1}, x_{2}, \ldots, x_{n}\right)}~P\left(x_{1}, x_{2}, \ldots, x_{n}\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: 19 operand: 6
2	Operation	operator: 4 operands: 5
3	ExprTuple	6
4	Literal
5	ExprTuple	42, 7
6	Lambda	parameters: 8 body: 9
7	Literal
8	ExprTuple	37, 32
9	Conditional	value: 10 condition: 11
10	Operation	operator: 12 operand: 16
11	Operation	operator: 14 operand: 17
12	Literal
13	ExprTuple	16
14	Literal
15	ExprTuple	17
16	Lambda	parameters: 24 body: 18
17	Operation	operator: 19 operand: 23
18	Conditional	value: 21 condition: 22
19	Literal
20	ExprTuple	23
21	Operation	operator: 37 operands: 24
22	Operation	operator: 32 operands: 24
23	Lambda	parameters: 38 body: 25
24	ExprTuple	26
25	Conditional	value: 27 condition: 28
26	ExprRange	lambda_map: 29 start_index: 41 end_index: 42
27	Operation	operator: 30 operands: 31
28	Operation	operator: 32 operands: 38
29	Lambda	parameter: 46 body: 33
30	Literal
31	ExprTuple	34, 35
32	Variable
33	IndexedVar	variable: 36 index: 46
34	Operation	operator: 37 operands: 38
35	Literal
36	Variable
37	Variable
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