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 B, Conditional, ExprTuple, Lambda, l, m, n
from proveit.core_expr_types import A_1_to_l, C_1_to_m, D_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, C_1_to_m, D_1_to_n], instance_expr = Or(A_1_to_l, C_1_to_m, B, D_1_to_n), condition = Or(A_1_to_l, B, C_1_to_m, D_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, C_{1}, C_{2}, \ldots, C_{m}, D_{1}, D_{2}, \ldots, D_{n}~|~A_{1} \lor  A_{2} \lor  \ldots \lor  A_{l} \lor B\lor C_{1} \lor  C_{2} \lor  \ldots \lor  C_{m}\lor D_{1} \lor  D_{2} \lor  \ldots \lor  D_{n}}~\left(A_{1} \lor  A_{2} \lor  \ldots \lor  A_{l}\lor C_{1} \lor  C_{2} \lor  \ldots \lor  C_{m} \lor B\lor D_{1} \lor  D_{2} \lor  \ldots \lor  D_{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, 32, 35
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: 24 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	32, 21
17	Literal
18	ExprTuple	35, 21
19	Operation	operator: 23 operands: 22
20	Operation	operator: 23 operands: 24
21	Literal
22	ExprTuple	25, 27, 26, 28
23	Literal
24	ExprTuple	25, 26, 27, 28
25	ExprRange	lambda_map: 29 start_index: 34 end_index: 30
26	Variable
27	ExprRange	lambda_map: 31 start_index: 34 end_index: 32
28	ExprRange	lambda_map: 33 start_index: 34 end_index: 35
29	Lambda	parameter: 43 body: 36
30	Variable
31	Lambda	parameter: 43 body: 37
32	Variable
33	Lambda	parameter: 43 body: 38
34	Literal
35	Variable
36	IndexedVar	variable: 39 index: 43
37	IndexedVar	variable: 40 index: 43
38	IndexedVar	variable: 41 index: 43
39	Variable
40	Variable
41	Variable
42	ExprTuple	43
43	Variable