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 ExprTuple, Lambda, P, Px, Q, Qx, x
from proveit.core_expr_types import Qk_implies_Pk_a1_to_an, a_1_to_n
from proveit.logic import Forall, Set

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([a_1_to_n], 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)))

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(\left(a_{1}, a_{2}, \ldots, a_{n}\right) \mapsto \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]\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	parameters: 36 body: 2
2	Operation	operator: 9 operand: 4
3	ExprTuple	4
4	Lambda	parameters: 5 body: 6
5	ExprTuple	31, 30
6	Conditional	value: 7 condition: 8
7	Operation	operator: 9 operand: 12
8	Operation	operator: 19 operands: 11
9	Literal
10	ExprTuple	12
11	ExprTuple	13
12	Lambda	parameter: 34 body: 14
13	ExprRange	lambda_map: 15 start_index: 39 end_index: 40
14	Conditional	value: 16 condition: 17
15	Lambda	parameter: 44 body: 18
16	Operation	operator: 31 operand: 34
17	Operation	operator: 19 operands: 20
18	Operation	operator: 21 operands: 22
19	Literal
20	ExprTuple	23, 24
21	Literal
22	ExprTuple	25, 26
23	Operation	operator: 27 operands: 28
24	Operation	operator: 30 operand: 34
25	Operation	operator: 30 operand: 41
26	Operation	operator: 31 operand: 41
27	Literal
28	ExprTuple	34, 33
29	ExprTuple	34
30	Variable
31	Variable
32	ExprTuple	41
33	Operation	operator: 35 operands: 36
34	Variable
35	Literal
36	ExprTuple	37
37	ExprRange	lambda_map: 38 start_index: 39 end_index: 40
38	Lambda	parameter: 44 body: 41
39	Literal
40	Variable
41	IndexedVar	variable: 42 index: 44
42	Variable
43	ExprTuple	44
44	Variable