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_exists_in_A_Px_st_Qx, general_exists_in_B_Py_st_Qy

# build up the expression from sub-expressions
expr = Implies(general_exists_in_A_Px_st_Qx, general_exists_in_B_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[\exists_{x_{1}, x_{2}, \ldots, x_{n} \in A~|~Q\left(x_{1}, x_{2}, \ldots, x_{n}\right)}~P\left(x_{1}, x_{2}, \ldots, x_{n}\right)\right] \Rightarrow  \\ \left[\exists_{y_{1}, y_{2}, \ldots, y_{n} \in B~|~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: 6 operand: 8
4	Operation	operator: 6 operand: 9
5	ExprTuple	8
6	Literal
7	ExprTuple	9
8	Lambda	parameters: 25 body: 10
9	Lambda	parameters: 28 body: 11
10	Conditional	value: 12 condition: 13
11	Conditional	value: 14 condition: 15
12	Operation	operator: 17 operands: 25
13	Operation	operator: 18 operands: 16
14	Operation	operator: 17 operands: 28
15	Operation	operator: 18 operands: 19
16	ExprTuple	20, 21
17	Variable
18	Literal
19	ExprTuple	22, 23
20	ExprRange	lambda_map: 24 start_index: 38 end_index: 39
21	Operation	operator: 27 operands: 25
22	ExprRange	lambda_map: 26 start_index: 38 end_index: 39
23	Operation	operator: 27 operands: 28
24	Lambda	parameter: 47 body: 29
25	ExprTuple	30
26	Lambda	parameter: 47 body: 31
27	Variable
28	ExprTuple	32
29	Operation	operator: 35 operands: 33
30	ExprRange	lambda_map: 34 start_index: 38 end_index: 39
31	Operation	operator: 35 operands: 36
32	ExprRange	lambda_map: 37 start_index: 38 end_index: 39
33	ExprTuple	41, 40
34	Lambda	parameter: 47 body: 41
35	Literal
36	ExprTuple	43, 42
37	Lambda	parameter: 47 body: 43
38	Literal
39	Variable
40	Variable
41	IndexedVar	variable: 44 index: 47
42	Variable
43	IndexedVar	variable: 45 index: 47
44	Variable
45	Variable
46	ExprTuple	47
47	Variable