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 A, Conditional, ExprRange, ExprTuple, IndexedVar, Lambda, Variable, m
from proveit.core_expr_types import A_1_to_m
from proveit.logic import And, Boolean, Forall, InSet, Or
from proveit.numbers import Add, NaturalPos, one, two

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(A, sub_expr1)
sub_expr3 = Add(m, one)
expr = ExprTuple(Lambda(m, Conditional(Forall(instance_param_or_params = [ExprRange(sub_expr1, sub_expr2, one, Add(m, two))], instance_expr = InSet(Or(ExprRange(sub_expr1, sub_expr2, one, sub_expr3)), Boolean), condition = ExprRange(sub_expr1, InSet(sub_expr2, Boolean), one, sub_expr3)), And(InSet(m, NaturalPos), Forall(instance_param_or_params = [A_1_to_m], instance_expr = InSet(Or(A_1_to_m), Boolean), domain = Boolean)))))

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(m \mapsto \left\{\forall_{A_{1}, A_{2}, \ldots, A_{m + 2}~|~\left(A_{1} \in \mathbb{B}\right), \left(A_{2} \in \mathbb{B}\right), \ldots, \left(A_{m + 1} \in \mathbb{B}\right)}~\left(\left(A_{1} \lor  A_{2} \lor  \ldots \lor  A_{m + 1}\right) \in \mathbb{B}\right) \textrm{ if } m \in \mathbb{N}^+ ,  \forall_{A_{1}, A_{2}, \ldots, A_{m} \in \mathbb{B}}~\left(\left(A_{1} \lor  A_{2} \lor  \ldots \lor  A_{m}\right) \in \mathbb{B}\right)\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	parameter: 48 body: 3
2	ExprTuple	48
3	Conditional	value: 4 condition: 5
4	Operation	operator: 14 operand: 8
5	Operation	operator: 33 operands: 7
6	ExprTuple	8
7	ExprTuple	9, 10
8	Lambda	parameters: 11 body: 12
9	Operation	operator: 49 operands: 13
10	Operation	operator: 14 operand: 20
11	ExprTuple	16
12	Conditional	value: 17 condition: 18
13	ExprTuple	48, 19
14	Literal
15	ExprTuple	20
16	ExprRange	lambda_map: 46 start_index: 47 end_index: 21
17	Operation	operator: 49 operands: 22
18	Operation	operator: 33 operands: 23
19	Literal
20	Lambda	parameters: 40 body: 24
21	Operation	operator: 42 operands: 25
22	ExprTuple	26, 52
23	ExprTuple	27
24	Conditional	value: 28 condition: 29
25	ExprTuple	48, 30
26	Operation	operator: 39 operands: 31
27	ExprRange	lambda_map: 41 start_index: 47 end_index: 38
28	Operation	operator: 49 operands: 32
29	Operation	operator: 33 operands: 34
30	Literal
31	ExprTuple	35
32	ExprTuple	36, 52
33	Literal
34	ExprTuple	37
35	ExprRange	lambda_map: 46 start_index: 47 end_index: 38
36	Operation	operator: 39 operands: 40
37	ExprRange	lambda_map: 41 start_index: 47 end_index: 48
38	Operation	operator: 42 operands: 43
39	Literal
40	ExprTuple	44
41	Lambda	parameter: 55 body: 45
42	Literal
43	ExprTuple	48, 47
44	ExprRange	lambda_map: 46 start_index: 47 end_index: 48
45	Operation	operator: 49 operands: 50
46	Lambda	parameter: 55 body: 51
47	Literal
48	Variable
49	Literal
50	ExprTuple	51, 52
51	IndexedVar	variable: 53 index: 55
52	Literal
53	Variable
54	ExprTuple	55
55	Variable