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 Conditional, ExprRange, Function, P, Pk, Variable, i, j, k
from proveit.logic import And, Equals, Exists, Forall, InSet, Or
from proveit.numbers import Add, Integer, Interval, LessEq, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(Forall(instance_param_or_params = [P], instance_expr = Equals(Or(ExprRange(sub_expr1, Function(P, [sub_expr1]), i, j)), Exists(instance_param_or_params = [k], instance_expr = Pk, domain = Interval(i, j))), condition = LessEq(i, Add(j, one))), And(InSet(i, Integer), InSet(j, Integer)))

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_{P~|~i \leq \left(j + 1\right)}~\left(\left(P\left(i\right) \lor  P\left(i + 1\right) \lor  \ldots \lor  P\left(j\right)\right) = \left[\exists_{k \in \{i~\ldotp \ldotp~j\}}~P\left(k\right)\right]\right) \textrm{ if } i \in \mathbb{Z} ,  j \in \mathbb{Z}\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: 3 operand: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	8, 9
7	Lambda	parameter: 39 body: 11
8	Operation	operator: 41 operands: 12
9	Operation	operator: 41 operands: 13
10	ExprTuple	39
11	Conditional	value: 14 condition: 15
12	ExprTuple	48, 16
13	ExprTuple	49, 16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 19 operands: 20
16	Literal
17	Literal
18	ExprTuple	21, 22
19	Literal
20	ExprTuple	48, 23
21	Operation	operator: 24 operands: 25
22	Operation	operator: 26 operand: 31
23	Operation	operator: 28 operands: 29
24	Literal
25	ExprTuple	30
26	Literal
27	ExprTuple	31
28	Literal
29	ExprTuple	49, 32
30	ExprRange	lambda_map: 33 start_index: 48 end_index: 49
31	Lambda	parameter: 44 body: 34
32	Literal
33	Lambda	parameter: 43 body: 35
34	Conditional	value: 36 condition: 37
35	Operation	operator: 39 operand: 43
36	Operation	operator: 39 operand: 44
37	Operation	operator: 41 operands: 42
38	ExprTuple	43
39	Variable
40	ExprTuple	44
41	Literal
42	ExprTuple	44, 45
43	Variable
44	Variable
45	Operation	operator: 46 operands: 47
46	Literal
47	ExprTuple	48, 49
48	Variable
49	Variable