Expression of type ExprTuple

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