Expression of type Conditional

from the theory of proveit.logic.booleans.conjunction

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, Forall, Implies, InSet
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 = Implies(Forall(instance_param_or_params = [k], instance_expr = Pk, domain = Interval(i, j)), And(ExprRange(sub_expr1, Function(P, [sub_expr1]), 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[\forall_{k \in \{i~\ldotp \ldotp~j\}}~P\left(k\right)\right] \Rightarrow \left(P\left(i\right) \land  P\left(i + 1\right) \land  \ldots \land  P\left(j\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: 22 operand: 5
2	Operation	operator: 24 operands: 4
3	ExprTuple	5
4	ExprTuple	6, 7
5	Lambda	parameter: 39 body: 9
6	Operation	operator: 37 operands: 10
7	Operation	operator: 37 operands: 11
8	ExprTuple	39
9	Conditional	value: 12 condition: 13
10	ExprTuple	46, 14
11	ExprTuple	47, 14
12	Operation	operator: 15 operands: 16
13	Operation	operator: 17 operands: 18
14	Literal
15	Literal
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	46, 21
19	Operation	operator: 22 operand: 28
20	Operation	operator: 24 operands: 25
21	Operation	operator: 26 operands: 27
22	Literal
23	ExprTuple	28
24	Literal
25	ExprTuple	29
26	Literal
27	ExprTuple	47, 30
28	Lambda	parameter: 41 body: 31
29	ExprRange	lambda_map: 32 start_index: 46 end_index: 47
30	Literal
31	Conditional	value: 33 condition: 34
32	Lambda	parameter: 43 body: 35
33	Operation	operator: 39 operand: 41
34	Operation	operator: 37 operands: 38
35	Operation	operator: 39 operand: 43
36	ExprTuple	41
37	Literal
38	ExprTuple	41, 42
39	Variable
40	ExprTuple	43
41	Variable
42	Operation	operator: 44 operands: 45
43	Variable
44	Literal
45	ExprTuple	46, 47
46	Variable
47	Variable