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, n
from proveit.logic import Forall, Implies, InSet, Not
from proveit.logic.booleans.quantification import general_exists_Px_st_Qx, general_notexists_Py_st_Qy
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(n, Conditional(Forall(instance_param_or_params = [P, Q], instance_expr = Implies(Not(general_exists_Px_st_Qx), general_notexists_Py_st_Qy).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}~\left(\begin{array}{c} \begin{array}{l} (\lnot \left[\exists_{x_{1}, x_{2}, \ldots, x_{n}~|~Q\left(x_{1}, x_{2}, \ldots, x_{n}\right)}~P\left(x_{1}, x_{2}, \ldots, x_{n}\right)\right]) \Rightarrow  \\ \left[\nexists_{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] \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: 41 body: 3
2	ExprTuple	41
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 10
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	41, 11
10	Lambda	parameters: 12 body: 13
11	Literal
12	ExprTuple	33, 34
13	Operation	operator: 14 operands: 15
14	Literal
15	ExprTuple	16, 17
16	Operation	operator: 18 operand: 21
17	Operation	operator: 20 operand: 25
18	Literal
19	ExprTuple	21
20	Literal
21	Operation	operator: 22 operand: 25
22	Literal
23	ExprTuple	25
24	Conditional	value: 26 condition: 27
25	Lambda	parameters: 35 body: 28
26	Operation	operator: 33 operands: 29
27	Operation	operator: 34 operands: 29
28	Conditional	value: 30 condition: 31
29	ExprTuple	32
30	Operation	operator: 33 operands: 35
31	Operation	operator: 34 operands: 35
32	ExprRange	lambda_map: 36 start_index: 40 end_index: 41
33	Variable
34	Variable
35	ExprTuple	37
36	Lambda	parameter: 46 body: 38
37	ExprRange	lambda_map: 39 start_index: 40 end_index: 41
38	IndexedVar	variable: 42 index: 46
39	Lambda	parameter: 46 body: 43
40	Literal
41	Variable
42	Variable
43	IndexedVar	variable: 44 index: 46
44	Variable
45	ExprTuple	46
46	Variable