Expression of type Implies

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 Implies
from proveit.logic.booleans.quantification import general_forall_Px_if_Qx, general_notexists_notPy_st_Qy

# build up the expression from sub-expressions
expr = Implies(general_forall_Px_if_Qx, general_notexists_notPy_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[\forall_{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)}~(\lnot 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: 9
4	Operation	operator: 7 operand: 10
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	10
9	Lambda	parameters: 17 body: 11
10	Lambda	parameters: 25 body: 12
11	Conditional	value: 13 condition: 14
12	Conditional	value: 15 condition: 16
13	Operation	operator: 24 operands: 17
14	Operation	operator: 20 operands: 17
15	Operation	operator: 18 operand: 22
16	Operation	operator: 20 operands: 25
17	ExprTuple	21
18	Literal
19	ExprTuple	22
20	Variable
21	ExprRange	lambda_map: 23 start_index: 30 end_index: 31
22	Operation	operator: 24 operands: 25
23	Lambda	parameter: 35 body: 26
24	Variable
25	ExprTuple	27
26	IndexedVar	variable: 28 index: 35
27	ExprRange	lambda_map: 29 start_index: 30 end_index: 31
28	Variable
29	Lambda	parameter: 35 body: 32
30	Literal
31	Variable
32	IndexedVar	variable: 33 index: 35
33	Variable
34	ExprTuple	35
35	Variable