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 A, Conditional, ExprRange, Variable, i, j
from proveit.logic import And, Forall, InSet
from proveit.numbers import Add, Integer, LessEq, one

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [A], instance_expr = And(ExprRange(Variable("_a", latex_format = r"{_{-}a}"), A, i, j)), conditions = [A, 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_{A~|~A, i \leq \left(j + 1\right)}~\left(A \land  A \land  ..\left(j - i - 2\right) \times.. \land  A\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: 6
2	Operation	operator: 18 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Lambda	parameter: 26 body: 10
7	Operation	operator: 12 operands: 11
8	Operation	operator: 12 operands: 13
9	ExprTuple	26
10	Conditional	value: 14 condition: 15
11	ExprTuple	27, 16
12	Literal
13	ExprTuple	32, 16
14	Operation	operator: 18 operands: 17
15	Operation	operator: 18 operands: 19
16	Literal
17	ExprTuple	20
18	Literal
19	ExprTuple	26, 21
20	ExprRange	lambda_map: 22 start_index: 27 end_index: 32
21	Operation	operator: 23 operands: 24
22	Lambda	parameter: 29 body: 26
23	Literal
24	ExprTuple	27, 28
25	ExprTuple	29
26	Variable
27	Variable
28	Operation	operator: 30 operands: 31
29	Variable
30	Literal
31	ExprTuple	32, 33
32	Variable
33	Literal