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 Conditional, P, Q, R, n
from proveit.logic import Forall, Implies, InSet
from proveit.logic.booleans.quantification import general_exists_Py_st_Qy, general_exists_Rz_st_Qz, general_forall_st_Qx__Px_implies_Rx
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [P, Q, R], instance_expr = Implies(general_forall_st_Qx__Px_implies_Rx, Implies(general_exists_Py_st_Qy, general_exists_Rz_st_Qz).with_wrapping_at(2)).with_wrapping_at(2)), InSet(n, NaturalPos))

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\{\forall_{P, Q, R}~\left(\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)}~\left(P\left(x_{1}, x_{2}, \ldots, x_{n}\right) \Rightarrow R\left(x_{1}, x_{2}, \ldots, x_{n}\right)\right)\right] \Rightarrow  \\ \left(\begin{array}{c} \begin{array}{l} \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] \Rightarrow  \\ \left[\exists_{z_{1}, z_{2}, \ldots, z_{n}~|~Q\left(z_{1}, z_{2}, \ldots, z_{n}\right)}~R\left(z_{1}, z_{2}, \ldots, z_{n}\right)\right] \end{array} \end{array}\right) \end{array} \end{array}\right) \textrm{ if } n \in \mathbb{N}^+\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: 13 operand: 6
2	Operation	operator: 4 operands: 5
3	ExprTuple	6
4	Literal
5	ExprTuple	50, 7
6	Lambda	parameters: 8 body: 9
7	Literal
8	ExprTuple	38, 41, 40
9	Operation	operator: 27 operands: 10
10	ExprTuple	11, 12
11	Operation	operator: 13 operand: 16
12	Operation	operator: 27 operands: 15
13	Literal
14	ExprTuple	16
15	ExprTuple	17, 18
16	Lambda	parameters: 37 body: 19
17	Operation	operator: 21 operand: 25
18	Operation	operator: 21 operand: 26
19	Conditional	value: 23 condition: 24
20	ExprTuple	25
21	Literal
22	ExprTuple	26
23	Operation	operator: 27 operands: 28
24	Operation	operator: 41 operands: 37
25	Lambda	parameters: 39 body: 29
26	Lambda	parameters: 42 body: 30
27	Literal
28	ExprTuple	31, 32
29	Conditional	value: 33 condition: 34
30	Conditional	value: 35 condition: 36
31	Operation	operator: 38 operands: 37
32	Operation	operator: 40 operands: 37
33	Operation	operator: 38 operands: 39
34	Operation	operator: 41 operands: 39
35	Operation	operator: 40 operands: 42
36	Operation	operator: 41 operands: 42
37	ExprTuple	43
38	Variable
39	ExprTuple	44
40	Variable
41	Variable
42	ExprTuple	45
43	ExprRange	lambda_map: 46 start_index: 49 end_index: 50
44	ExprRange	lambda_map: 47 start_index: 49 end_index: 50
45	ExprRange	lambda_map: 48 start_index: 49 end_index: 50
46	Lambda	parameter: 58 body: 51
47	Lambda	parameter: 58 body: 52
48	Lambda	parameter: 58 body: 53
49	Literal
50	Variable
51	IndexedVar	variable: 54 index: 58
52	IndexedVar	variable: 55 index: 58
53	IndexedVar	variable: 56 index: 58
54	Variable
55	Variable
56	Variable
57	ExprTuple	58
58	Variable