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, m, n
from proveit.core_expr_types import A_1_to_m, C_1_to_n
from proveit.logic import And, Boolean, Forall, InSet, Or
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, B, C_1_to_n], instance_expr = Or(A_1_to_m, B, C_1_to_n), domain = Boolean, condition = B), 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}, B, C_{1}, C_{2}, \ldots, C_{n} \in \mathbb{B}~|~B}~\left(A_{1} \lor  A_{2} \lor  \ldots \lor  A_{m} \lor B\lor C_{1} \lor  C_{2} \lor  \ldots \lor  C_{n}\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	30, 34
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 20 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	10, 11
9	Lambda	parameters: 19 body: 12
10	Operation	operator: 39 operands: 13
11	Operation	operator: 39 operands: 14
12	Conditional	value: 15 condition: 16
13	ExprTuple	30, 17
14	ExprTuple	34, 17
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operands: 21
17	Literal
18	Literal
19	ExprTuple	22, 36, 23
20	Literal
21	ExprTuple	24, 25, 26, 36
22	ExprRange	lambda_map: 27 start_index: 33 end_index: 30
23	ExprRange	lambda_map: 28 start_index: 33 end_index: 34
24	ExprRange	lambda_map: 29 start_index: 33 end_index: 30
25	Operation	operator: 39 operands: 31
26	ExprRange	lambda_map: 32 start_index: 33 end_index: 34
27	Lambda	parameter: 47 body: 41
28	Lambda	parameter: 47 body: 42
29	Lambda	parameter: 47 body: 35
30	Variable
31	ExprTuple	36, 43
32	Lambda	parameter: 47 body: 37
33	Literal
34	Variable
35	Operation	operator: 39 operands: 38
36	Variable
37	Operation	operator: 39 operands: 40
38	ExprTuple	41, 43
39	Literal
40	ExprTuple	42, 43
41	IndexedVar	variable: 44 index: 47
42	IndexedVar	variable: 45 index: 47
43	Literal
44	Variable
45	Variable
46	ExprTuple	47
47	Variable