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