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, 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(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(\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), \left[\forall_{x \in \left\{a_{1}, a_{2}, \ldots, a_{n}\right\}}~P\left(x\right)\right] = \bot\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 13 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 17
6	ExprRange	lambda_map: 8 start_index: 31 end_index: 32
7	Operation	operator: 9 operand: 12
8	Lambda	parameter: 36 body: 11
9	Literal
10	ExprTuple	12
11	Operation	operator: 13 operands: 14
12	Lambda	parameter: 25 body: 15
13	Literal
14	ExprTuple	16, 17
15	Conditional	value: 18 condition: 19
16	Operation	operator: 21 operand: 33
17	Literal
18	Operation	operator: 21 operand: 25
19	Operation	operator: 23 operands: 24
20	ExprTuple	33
21	Variable
22	ExprTuple	25
23	Literal
24	ExprTuple	25, 26
25	Variable
26	Operation	operator: 27 operands: 28
27	Literal
28	ExprTuple	29
29	ExprRange	lambda_map: 30 start_index: 31 end_index: 32
30	Lambda	parameter: 36 body: 33
31	Literal
32	Variable
33	IndexedVar	variable: 34 index: 36
34	Variable
35	ExprTuple	36
36	Variable