Expression of type Conditional

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, IndexedVar, 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 = 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\{\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..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 11 operand: 5
2	Operation	operator: 30 operands: 4
3	ExprTuple	5
4	ExprTuple	6, 7
5	Lambda	parameters: 8 body: 9
6	Operation	operator: 46 operands: 10
7	Operation	operator: 11 operand: 17
8	ExprTuple	13
9	Conditional	value: 14 condition: 15
10	ExprTuple	45, 16
11	Literal
12	ExprTuple	17
13	ExprRange	lambda_map: 43 start_index: 44 end_index: 18
14	Operation	operator: 46 operands: 19
15	Operation	operator: 30 operands: 20
16	Literal
17	Lambda	parameters: 37 body: 21
18	Operation	operator: 39 operands: 22
19	ExprTuple	23, 49
20	ExprTuple	24
21	Conditional	value: 25 condition: 26
22	ExprTuple	45, 27
23	Operation	operator: 36 operands: 28
24	ExprRange	lambda_map: 38 start_index: 44 end_index: 35
25	Operation	operator: 46 operands: 29
26	Operation	operator: 30 operands: 31
27	Literal
28	ExprTuple	32
29	ExprTuple	33, 49
30	Literal
31	ExprTuple	34
32	ExprRange	lambda_map: 43 start_index: 44 end_index: 35
33	Operation	operator: 36 operands: 37
34	ExprRange	lambda_map: 38 start_index: 44 end_index: 45
35	Operation	operator: 39 operands: 40
36	Literal
37	ExprTuple	41
38	Lambda	parameter: 52 body: 42
39	Literal
40	ExprTuple	45, 44
41	ExprRange	lambda_map: 43 start_index: 44 end_index: 45
42	Operation	operator: 46 operands: 47
43	Lambda	parameter: 52 body: 48
44	Literal
45	Variable
46	Literal
47	ExprTuple	48, 49
48	IndexedVar	variable: 50 index: 52
49	Literal
50	Variable
51	ExprTuple	52
52	Variable