Expression of type ExprTuple

from the theory of proveit.logic.booleans.disjunction

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, l, m, n
from proveit.core_expr_types import A_1_to_l, B_1_to_m, C_1_to_n
from proveit.logic import And, Forall, InSet, Or
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([l, m, n], Conditional(Forall(instance_param_or_params = [A_1_to_l, B_1_to_m, C_1_to_n], instance_expr = Or(A_1_to_l, Or(B_1_to_m), C_1_to_n), condition = Or(A_1_to_l, B_1_to_m, C_1_to_n)), And(InSet(l, Natural), InSet(m, Natural), 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(\left(l, m, n\right) \mapsto \left\{\forall_{A_{1}, A_{2}, \ldots, A_{l}, B_{1}, B_{2}, \ldots, B_{m}, C_{1}, C_{2}, \ldots, C_{n}~|~A_{1} \lor  A_{2} \lor  \ldots \lor  A_{l}\lor B_{1} \lor  B_{2} \lor  \ldots \lor  B_{m}\lor C_{1} \lor  C_{2} \lor  \ldots \lor  C_{n}}~\left(A_{1} \lor  A_{2} \lor  \ldots \lor  A_{l} \lor \left(B_{1} \lor  B_{2} \lor  \ldots \lor  B_{m}\right)\lor C_{1} \lor  C_{2} \lor  \ldots \lor  C_{n}\right) \textrm{ if } l \in \mathbb{N} ,  m \in \mathbb{N} ,  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	parameters: 2 body: 3
2	ExprTuple	30, 38, 32
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 10
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	11, 12, 13
10	Lambda	parameters: 23 body: 14
11	Operation	operator: 17 operands: 15
12	Operation	operator: 17 operands: 16
13	Operation	operator: 17 operands: 18
14	Conditional	value: 19 condition: 20
15	ExprTuple	30, 21
16	ExprTuple	38, 21
17	Literal
18	ExprTuple	32, 21
19	Operation	operator: 27 operands: 22
20	Operation	operator: 27 operands: 23
21	Literal
22	ExprTuple	25, 24, 26
23	ExprTuple	25, 33, 26
24	Operation	operator: 27 operands: 28
25	ExprRange	lambda_map: 29 start_index: 37 end_index: 30
26	ExprRange	lambda_map: 31 start_index: 37 end_index: 32
27	Literal
28	ExprTuple	33
29	Lambda	parameter: 44 body: 34
30	Variable
31	Lambda	parameter: 44 body: 35
32	Variable
33	ExprRange	lambda_map: 36 start_index: 37 end_index: 38
34	IndexedVar	variable: 39 index: 44
35	IndexedVar	variable: 40 index: 44
36	Lambda	parameter: 44 body: 41
37	Literal
38	Variable
39	Variable
40	Variable
41	IndexedVar	variable: 42 index: 44
42	Variable
43	ExprTuple	44
44	Variable