Expression of type Forall

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 P, Q
from proveit.logic import Forall, Implies, Not
from proveit.logic.booleans.quantification import general_exists_Px_st_Qx, general_notexists_Py_st_Qy

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [P, Q], instance_expr = Implies(Not(general_exists_Px_st_Qx), general_notexists_Py_st_Qy).with_wrapping_at(2))

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())

\forall_{P, Q}~\left(\begin{array}{c} \begin{array}{l} (\lnot \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]) \Rightarrow  \\ \left[\nexists_{y_{1}, y_{2}, \ldots, y_{n}~|~Q\left(y_{1}, y_{2}, \ldots, y_{n}\right)}~P\left(y_{1}, y_{2}, \ldots, y_{n}\right)\right] \end{array} \end{array}\right)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

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