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, P, Q, n
from proveit.logic import Forall, Implies, InSet, SubsetEq
from proveit.logic.booleans.quantification import general_exists_in_A_Px_st_Qx, general_exists_in_B_Py_st_Qy
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [P, Q, A, B], instance_expr = Implies(general_exists_in_A_Px_st_Qx, general_exists_in_B_Py_st_Qy).with_wrapping_at(2), condition = SubsetEq(A, B)), InSet(n, NaturalPos))

# 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\{\forall_{P, Q, A, B~|~A \subseteq B}~\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}\right) \textrm{ if } n \in \mathbb{N}^+\right..

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operand: 6
2	Operation	operator: 48 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	52, 7
6	Lambda	parameters: 8 body: 9
7	Literal
8	ExprTuple	30, 40, 53, 55
9	Conditional	value: 10 condition: 11
10	Operation	operator: 12 operands: 13
11	Operation	operator: 14 operands: 15
12	Literal
13	ExprTuple	16, 17
14	Literal
15	ExprTuple	53, 55
16	Operation	operator: 19 operand: 21
17	Operation	operator: 19 operand: 22
18	ExprTuple	21
19	Literal
20	ExprTuple	22
21	Lambda	parameters: 38 body: 23
22	Lambda	parameters: 41 body: 24
23	Conditional	value: 25 condition: 26
24	Conditional	value: 27 condition: 28
25	Operation	operator: 30 operands: 38
26	Operation	operator: 31 operands: 29
27	Operation	operator: 30 operands: 41
28	Operation	operator: 31 operands: 32
29	ExprTuple	33, 34
30	Variable
31	Literal
32	ExprTuple	35, 36
33	ExprRange	lambda_map: 37 start_index: 51 end_index: 52
34	Operation	operator: 40 operands: 38
35	ExprRange	lambda_map: 39 start_index: 51 end_index: 52
36	Operation	operator: 40 operands: 41
37	Lambda	parameter: 60 body: 42
38	ExprTuple	43
39	Lambda	parameter: 60 body: 44
40	Variable
41	ExprTuple	45
42	Operation	operator: 48 operands: 46
43	ExprRange	lambda_map: 47 start_index: 51 end_index: 52
44	Operation	operator: 48 operands: 49
45	ExprRange	lambda_map: 50 start_index: 51 end_index: 52
46	ExprTuple	54, 53
47	Lambda	parameter: 60 body: 54
48	Literal
49	ExprTuple	56, 55
50	Lambda	parameter: 60 body: 56
51	Literal
52	Variable
53	Variable
54	IndexedVar	variable: 57 index: 60
55	Variable
56	IndexedVar	variable: 58 index: 60
57	Variable
58	Variable
59	ExprTuple	60
60	Variable

Expression of type Conditional¶

from the theory of proveit.logic.booleans.quantification.existence¶

Expression of type Conditional ¶

from the theory of proveit.logic.booleans.quantification.existence ¶