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 Add, Integer, Interval, LessEq, one

# 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(Exists(instance_param_or_params = [k], instance_expr = Pk, domain = Interval(i, j)), Or(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(\left(i, j\right) \mapsto \left\{\forall_{P~|~i \leq \left(j + 1\right)}~\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)\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: 49 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: 43 body: 13
10	Operation	operator: 41 operands: 14
11	Operation	operator: 41 operands: 15
12	ExprTuple	43
13	Conditional	value: 16 condition: 17
14	ExprTuple	50, 18
15	ExprTuple	51, 18
16	Operation	operator: 19 operands: 20
17	Operation	operator: 21 operands: 22
18	Literal
19	Literal
20	ExprTuple	23, 24
21	Literal
22	ExprTuple	50, 25
23	Operation	operator: 26 operand: 32
24	Operation	operator: 28 operands: 29
25	Operation	operator: 30 operands: 31
26	Literal
27	ExprTuple	32
28	Literal
29	ExprTuple	33
30	Literal
31	ExprTuple	51, 34
32	Lambda	parameter: 45 body: 35
33	ExprRange	lambda_map: 36 start_index: 50 end_index: 51
34	Literal
35	Conditional	value: 37 condition: 38
36	Lambda	parameter: 47 body: 39
37	Operation	operator: 43 operand: 45
38	Operation	operator: 41 operands: 42
39	Operation	operator: 43 operand: 47
40	ExprTuple	45
41	Literal
42	ExprTuple	45, 46
43	Variable
44	ExprTuple	47
45	Variable
46	Operation	operator: 48 operands: 49
47	Variable
48	Literal
49	ExprTuple	50, 51
50	Variable
51	Variable