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_notPx_st_Qx, general_forall_Py_if_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(general_exists_notPx_st_Qx, Not(general_forall_Py_if_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} \left[\exists_{x_{1}, x_{2}, \ldots, x_{n}~|~Q\left(x_{1}, x_{2}, \ldots, x_{n}\right)}~(\lnot P\left(x_{1}, x_{2}, \ldots, x_{n}\right))\right] \Rightarrow  \\ (\lnot \left[\forall_{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: 43 body: 3
2	ExprTuple	43
3	Conditional	value: 4 condition: 5
4	Operation	operator: 23 operand: 9
5	Operation	operator: 7 operands: 8
6	ExprTuple	9
7	Literal
8	ExprTuple	43, 10
9	Lambda	parameters: 11 body: 12
10	Literal
11	ExprTuple	35, 36
12	Operation	operator: 13 operands: 14
13	Literal
14	ExprTuple	15, 16
15	Operation	operator: 17 operand: 20
16	Operation	operator: 28 operand: 21
17	Literal
18	ExprTuple	20
19	ExprTuple	21
20	Lambda	parameters: 34 body: 22
21	Operation	operator: 23 operand: 27
22	Conditional	value: 25 condition: 26
23	Literal
24	ExprTuple	27
25	Operation	operator: 28 operand: 31
26	Operation	operator: 36 operands: 34
27	Lambda	parameters: 37 body: 30
28	Literal
29	ExprTuple	31
30	Conditional	value: 32 condition: 33
31	Operation	operator: 35 operands: 34
32	Operation	operator: 35 operands: 37
33	Operation	operator: 36 operands: 37
34	ExprTuple	38
35	Variable
36	Variable
37	ExprTuple	39
38	ExprRange	lambda_map: 40 start_index: 42 end_index: 43
39	ExprRange	lambda_map: 41 start_index: 42 end_index: 43
40	Lambda	parameter: 49 body: 44
41	Lambda	parameter: 49 body: 45
42	Literal
43	Variable
44	IndexedVar	variable: 46 index: 49
45	IndexedVar	variable: 47 index: 49
46	Variable
47	Variable
48	ExprTuple	49
49	Variable