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 Conditional, ExprRange, ExprTuple, Function, Lambda, P, Pk, Variable, i, j, k
from proveit.logic import And, Exists, Forall, Implies, InSet, Or
from proveit.numbers import Integer, Interval

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Lambda([i, j], Conditional(Forall(instance_param_or_params = [P], instance_expr = Implies(Or(ExprRange(sub_expr1, Function(P, [sub_expr1]), i, j)), Exists(instance_param_or_params = [k], instance_expr = Pk, domain = Interval(i, j)))), 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(\left(i, j\right) \mapsto \left\{\forall_{P}~\left(\left(P\left(i\right) \lor  P\left(i + 1\right) \lor  \ldots \lor  P\left(j\right)\right) \Rightarrow \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..\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	parameters: 41 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	10, 11
9	Lambda	parameter: 33 body: 13
10	Operation	operator: 35 operands: 14
11	Operation	operator: 35 operands: 15
12	ExprTuple	33
13	Operation	operator: 16 operands: 17
14	ExprTuple	42, 18
15	ExprTuple	43, 18
16	Literal
17	ExprTuple	19, 20
18	Literal
19	Operation	operator: 21 operands: 22
20	Operation	operator: 23 operand: 26
21	Literal
22	ExprTuple	25
23	Literal
24	ExprTuple	26
25	ExprRange	lambda_map: 27 start_index: 42 end_index: 43
26	Lambda	parameter: 38 body: 28
27	Lambda	parameter: 37 body: 29
28	Conditional	value: 30 condition: 31
29	Operation	operator: 33 operand: 37
30	Operation	operator: 33 operand: 38
31	Operation	operator: 35 operands: 36
32	ExprTuple	37
33	Variable
34	ExprTuple	38
35	Literal
36	ExprTuple	38, 39
37	Variable
38	Variable
39	Operation	operator: 40 operands: 41
40	Literal
41	ExprTuple	42, 43
42	Variable
43	Variable