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, m, n
from proveit.core_expr_types import A_1_to_m, C_1_to_n
from proveit.logic import And, Boolean, Equals, Forall, InSet, Or, TRUE
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([m, n], Conditional(Forall(instance_param_or_params = [A_1_to_m, C_1_to_n], instance_expr = Equals(Or(A_1_to_m, TRUE, C_1_to_n), TRUE), domain = Boolean), And(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(m, n\right) \mapsto \left\{\forall_{A_{1}, A_{2}, \ldots, A_{m}, C_{1}, C_{2}, \ldots, C_{n} \in \mathbb{B}}~\left(\left(A_{1} \lor  A_{2} \lor  \ldots \lor  A_{m} \lor \top\lor C_{1} \lor  C_{2} \lor  \ldots \lor  C_{n}\right) = \top\right) \textrm{ if } 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	36, 39
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 21 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	10, 11
9	Lambda	parameters: 12 body: 13
10	Operation	operator: 41 operands: 14
11	Operation	operator: 41 operands: 15
12	ExprTuple	30, 32
13	Conditional	value: 16 condition: 17
14	ExprTuple	36, 18
15	ExprTuple	39, 18
16	Operation	operator: 19 operands: 20
17	Operation	operator: 21 operands: 22
18	Literal
19	Literal
20	ExprTuple	23, 31
21	Literal
22	ExprTuple	24, 25
23	Operation	operator: 26 operands: 27
24	ExprRange	lambda_map: 28 start_index: 38 end_index: 36
25	ExprRange	lambda_map: 29 start_index: 38 end_index: 39
26	Literal
27	ExprTuple	30, 31, 32
28	Lambda	parameter: 49 body: 33
29	Lambda	parameter: 49 body: 34
30	ExprRange	lambda_map: 35 start_index: 38 end_index: 36
31	Literal
32	ExprRange	lambda_map: 37 start_index: 38 end_index: 39
33	Operation	operator: 41 operands: 40
34	Operation	operator: 41 operands: 42
35	Lambda	parameter: 49 body: 43
36	Variable
37	Lambda	parameter: 49 body: 44
38	Literal
39	Variable
40	ExprTuple	43, 45
41	Literal
42	ExprTuple	44, 45
43	IndexedVar	variable: 46 index: 49
44	IndexedVar	variable: 47 index: 49
45	Literal
46	Variable
47	Variable
48	ExprTuple	49
49	Variable