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.core_expr_types import P__y_1_to_n, Q__y_1_to_n, y_1_to_n
from proveit.logic import Forall, InSet
from proveit.logic.booleans.quantification import general_exists_Px_st_Qx
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 = Forall(instance_param_or_params = [y_1_to_n], instance_expr = general_exists_Px_st_Qx, conditions = [P__y_1_to_n, Q__y_1_to_n])), 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[\forall_{y_{1}, y_{2}, \ldots, y_{n}~|~P\left(y_{1}, y_{2}, \ldots, y_{n}\right), Q\left(y_{1}, y_{2}, \ldots, y_{n}\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]\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: 39 body: 3
2	ExprTuple	39
3	Conditional	value: 4 condition: 5
4	Operation	operator: 13 operand: 9
5	Operation	operator: 7 operands: 8
6	ExprTuple	9
7	Literal
8	ExprTuple	39, 10
9	Lambda	parameters: 11 body: 12
10	Literal
11	ExprTuple	31, 32
12	Operation	operator: 13 operand: 15
13	Literal
14	ExprTuple	15
15	Lambda	parameters: 27 body: 16
16	Conditional	value: 17 condition: 18
17	Operation	operator: 19 operand: 23
18	Operation	operator: 21 operands: 22
19	Literal
20	ExprTuple	23
21	Literal
22	ExprTuple	24, 25
23	Lambda	parameters: 33 body: 26
24	Operation	operator: 31 operands: 27
25	Operation	operator: 32 operands: 27
26	Conditional	value: 28 condition: 29
27	ExprTuple	30
28	Operation	operator: 31 operands: 33
29	Operation	operator: 32 operands: 33
30	ExprRange	lambda_map: 34 start_index: 38 end_index: 39
31	Variable
32	Variable
33	ExprTuple	35
34	Lambda	parameter: 44 body: 36
35	ExprRange	lambda_map: 37 start_index: 38 end_index: 39
36	IndexedVar	variable: 40 index: 44
37	Lambda	parameter: 44 body: 41
38	Literal
39	Variable
40	Variable
41	IndexedVar	variable: 42 index: 44
42	Variable
43	ExprTuple	44
44	Variable