Expression of type ExprTuple

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, ExprTuple, Lambda, 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 = ExprTuple(Lambda(n, 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(n \mapsto \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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 53 body: 3
2	ExprTuple	53
3	Conditional	value: 4 condition: 5
4	Operation	operator: 16 operand: 9
5	Operation	operator: 7 operands: 8
6	ExprTuple	9
7	Literal
8	ExprTuple	53, 10
9	Lambda	parameters: 11 body: 12
10	Literal
11	ExprTuple	41, 44, 43
12	Operation	operator: 30 operands: 13
13	ExprTuple	14, 15
14	Operation	operator: 16 operand: 19
15	Operation	operator: 30 operands: 18
16	Literal
17	ExprTuple	19
18	ExprTuple	20, 21
19	Lambda	parameters: 40 body: 22
20	Operation	operator: 24 operand: 28
21	Operation	operator: 24 operand: 29
22	Conditional	value: 26 condition: 27
23	ExprTuple	28
24	Literal
25	ExprTuple	29
26	Operation	operator: 30 operands: 31
27	Operation	operator: 44 operands: 40
28	Lambda	parameters: 42 body: 32
29	Lambda	parameters: 45 body: 33
30	Literal
31	ExprTuple	34, 35
32	Conditional	value: 36 condition: 37
33	Conditional	value: 38 condition: 39
34	Operation	operator: 41 operands: 40
35	Operation	operator: 43 operands: 40
36	Operation	operator: 41 operands: 42
37	Operation	operator: 44 operands: 42
38	Operation	operator: 43 operands: 45
39	Operation	operator: 44 operands: 45
40	ExprTuple	46
41	Variable
42	ExprTuple	47
43	Variable
44	Variable
45	ExprTuple	48
46	ExprRange	lambda_map: 49 start_index: 52 end_index: 53
47	ExprRange	lambda_map: 50 start_index: 52 end_index: 53
48	ExprRange	lambda_map: 51 start_index: 52 end_index: 53
49	Lambda	parameter: 61 body: 54
50	Lambda	parameter: 61 body: 55
51	Lambda	parameter: 61 body: 56
52	Literal
53	Variable
54	IndexedVar	variable: 57 index: 61
55	IndexedVar	variable: 58 index: 61
56	IndexedVar	variable: 59 index: 61
57	Variable
58	Variable
59	Variable
60	ExprTuple	61
61	Variable