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 A, B, Conditional
from proveit.logic import Implies, SubsetEq
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 = Conditional(Implies(general_exists_in_A_Px_st_Qx, general_exists_in_B_Py_st_Qy).with_wrapping_at(2), SubsetEq(A, B))

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\{\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} \textrm{ if } A \subseteq B\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: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	44, 46
7	Operation	operator: 10 operand: 12
8	Operation	operator: 10 operand: 13
9	ExprTuple	12
10	Literal
11	ExprTuple	13
12	Lambda	parameters: 29 body: 14
13	Lambda	parameters: 32 body: 15
14	Conditional	value: 16 condition: 17
15	Conditional	value: 18 condition: 19
16	Operation	operator: 21 operands: 29
17	Operation	operator: 22 operands: 20
18	Operation	operator: 21 operands: 32
19	Operation	operator: 22 operands: 23
20	ExprTuple	24, 25
21	Variable
22	Literal
23	ExprTuple	26, 27
24	ExprRange	lambda_map: 28 start_index: 42 end_index: 43
25	Operation	operator: 31 operands: 29
26	ExprRange	lambda_map: 30 start_index: 42 end_index: 43
27	Operation	operator: 31 operands: 32
28	Lambda	parameter: 51 body: 33
29	ExprTuple	34
30	Lambda	parameter: 51 body: 35
31	Variable
32	ExprTuple	36
33	Operation	operator: 39 operands: 37
34	ExprRange	lambda_map: 38 start_index: 42 end_index: 43
35	Operation	operator: 39 operands: 40
36	ExprRange	lambda_map: 41 start_index: 42 end_index: 43
37	ExprTuple	45, 44
38	Lambda	parameter: 51 body: 45
39	Literal
40	ExprTuple	47, 46
41	Lambda	parameter: 51 body: 47
42	Literal
43	Variable
44	Variable
45	IndexedVar	variable: 48 index: 51
46	Variable
47	IndexedVar	variable: 49 index: 51
48	Variable
49	Variable
50	ExprTuple	51
51	Variable