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 Exists, Implies, Or
from proveit.numbers import Add, Interval, LessEq, one

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

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