Expression of type ExprTuple

from the theory of proveit.logic.sets.enumeration

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, Px, Q, Qx, n, x
from proveit.core_expr_types import Qk_implies_Pk_a1_to_an, a_1_to_n
from proveit.logic import Forall, InSet, Set
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(n, Conditional(Forall(instance_param_or_params = [a_1_to_n], instance_expr = Forall(instance_param_or_params = [P, Q], instance_expr = Forall(instance_param_or_params = [x], instance_expr = Px, domain = Set(a_1_to_n), condition = Qx), condition = Qk_implies_Pk_a1_to_an)), InSet(n, Natural))))

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_{a_{1}, a_{2}, \ldots, a_{n}}~\left[\forall_{P, Q~|~\left(Q\left(a_{1}\right) \Rightarrow P\left(a_{1}\right)\right), \left(Q\left(a_{2}\right) \Rightarrow P\left(a_{2}\right)\right), \ldots, \left(Q\left(a_{n}\right) \Rightarrow P\left(a_{n}\right)\right)}~\left[\forall_{x \in \left\{a_{1}, a_{2}, \ldots, a_{n}\right\}~|~Q\left(x\right)}~P\left(x\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: 48 body: 3
2	ExprTuple	48
3	Conditional	value: 4 condition: 5
4	Operation	operator: 17 operand: 8
5	Operation	operator: 35 operands: 7
6	ExprTuple	8
7	ExprTuple	48, 9
8	Lambda	parameters: 44 body: 10
9	Literal
10	Operation	operator: 17 operand: 12
11	ExprTuple	12
12	Lambda	parameters: 13 body: 14
13	ExprTuple	39, 38
14	Conditional	value: 15 condition: 16
15	Operation	operator: 17 operand: 20
16	Operation	operator: 27 operands: 19
17	Literal
18	ExprTuple	20
19	ExprTuple	21
20	Lambda	parameter: 42 body: 22
21	ExprRange	lambda_map: 23 start_index: 47 end_index: 48
22	Conditional	value: 24 condition: 25
23	Lambda	parameter: 52 body: 26
24	Operation	operator: 39 operand: 42
25	Operation	operator: 27 operands: 28
26	Operation	operator: 29 operands: 30
27	Literal
28	ExprTuple	31, 32
29	Literal
30	ExprTuple	33, 34
31	Operation	operator: 35 operands: 36
32	Operation	operator: 38 operand: 42
33	Operation	operator: 38 operand: 49
34	Operation	operator: 39 operand: 49
35	Literal
36	ExprTuple	42, 41
37	ExprTuple	42
38	Variable
39	Variable
40	ExprTuple	49
41	Operation	operator: 43 operands: 44
42	Variable
43	Literal
44	ExprTuple	45
45	ExprRange	lambda_map: 46 start_index: 47 end_index: 48
46	Lambda	parameter: 52 body: 49
47	Literal
48	Variable
49	IndexedVar	variable: 50 index: 52
50	Variable
51	ExprTuple	52
52	Variable