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 ExprRange, ExprTuple, Function, IndexedVar, Lambda, P, Px, Variable, a, n, x
from proveit.core_expr_types import a_1_to_n
from proveit.logic import Equals, FALSE, Forall, Or, Set
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Lambda(P, Equals(Or(ExprRange(sub_expr1, Equals(Function(P, [IndexedVar(a, sub_expr1)]), FALSE), one, n)), Equals(Forall(instance_param_or_params = [x], instance_expr = Px, domain = Set(a_1_to_n)), FALSE))))

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