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 A, B, Conditional, ExprTuple, Lambda, P, Q, n
from proveit.logic import Forall, Implies, InSet, SubsetEq
from proveit.logic.booleans.quantification import general_exists_in_A_Px_st_Qx, general_exists_in_B_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, A, B], instance_expr = Implies(general_exists_in_A_Px_st_Qx, general_exists_in_B_Py_st_Qy).with_wrapping_at(2), condition = SubsetEq(A, B)), 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, A, B~|~A \subseteq B}~\left(\begin{array}{c} \begin{array}{l} \left[\exists_{x_{1}, x_{2}, \ldots, x_{n} \in A~|~Q\left(x_{1}, x_{2}, \ldots, x_{n}\right)}~P\left(x_{1}, x_{2}, \ldots, x_{n}\right)\right] \Rightarrow  \\ \left[\exists_{y_{1}, y_{2}, \ldots, y_{n} \in B~|~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: 55 body: 3
2	ExprTuple	55
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 51 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	55, 10
9	Lambda	parameters: 11 body: 12
10	Literal
11	ExprTuple	33, 43, 56, 58
12	Conditional	value: 13 condition: 14
13	Operation	operator: 15 operands: 16
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	56, 58
19	Operation	operator: 22 operand: 24
20	Operation	operator: 22 operand: 25
21	ExprTuple	24
22	Literal
23	ExprTuple	25
24	Lambda	parameters: 41 body: 26
25	Lambda	parameters: 44 body: 27
26	Conditional	value: 28 condition: 29
27	Conditional	value: 30 condition: 31
28	Operation	operator: 33 operands: 41
29	Operation	operator: 34 operands: 32
30	Operation	operator: 33 operands: 44
31	Operation	operator: 34 operands: 35
32	ExprTuple	36, 37
33	Variable
34	Literal
35	ExprTuple	38, 39
36	ExprRange	lambda_map: 40 start_index: 54 end_index: 55
37	Operation	operator: 43 operands: 41
38	ExprRange	lambda_map: 42 start_index: 54 end_index: 55
39	Operation	operator: 43 operands: 44
40	Lambda	parameter: 63 body: 45
41	ExprTuple	46
42	Lambda	parameter: 63 body: 47
43	Variable
44	ExprTuple	48
45	Operation	operator: 51 operands: 49
46	ExprRange	lambda_map: 50 start_index: 54 end_index: 55
47	Operation	operator: 51 operands: 52
48	ExprRange	lambda_map: 53 start_index: 54 end_index: 55
49	ExprTuple	57, 56
50	Lambda	parameter: 63 body: 57
51	Literal
52	ExprTuple	59, 58
53	Lambda	parameter: 63 body: 59
54	Literal
55	Variable
56	Variable
57	IndexedVar	variable: 60 index: 63
58	Variable
59	IndexedVar	variable: 61 index: 63
60	Variable
61	Variable
62	ExprTuple	63
63	Variable