Expression of type Equals

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.logic import Equals, Not
from proveit.logic.booleans.quantification import general_exists_Py_st_Qy, general_notexists_Px_st_Qx

# build up the expression from sub-expressions
expr = Equals(general_notexists_Px_st_Qx, Not(general_exists_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())

\begin{array}{c} \begin{array}{l} \left[\nexists_{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] =  \\ (\lnot \left[\exists_{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}

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	(2)	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

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