Expression of type ExprTuple

from the theory of proveit.core_expr_types.tuples

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, ExprTuple, Lambda, f, i, j, k
from proveit.core_expr_types import partition_equiv
from proveit.logic import And, InSet
from proveit.numbers import Add, Natural, one, subtract

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([f, i, j, k], Conditional(partition_equiv, And(InSet(subtract(Add(j, one), i), Natural), InSet(subtract(k, j), Natural)))))

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(f, i, j, k\right) \mapsto \left\{\begin{array}{c} \begin{array}{l} \left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(k\right)\right) =  \\ \left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j\right),f\left(j + 1\right), f\left(j + 2\right), \ldots, f\left(k\right)\right) \end{array} \end{array} \textrm{ if } \left(\left(j + 1\right) - i\right) \in \mathbb{N} ,  \left(k - j\right) \in \mathbb{N}\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: 2 body: 3
2	ExprTuple	27, 40, 41, 31
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	12, 13
10	ExprTuple	14
11	ExprTuple	15, 16
12	Operation	operator: 18 operands: 17
13	Operation	operator: 18 operands: 19
14	ExprRange	lambda_map: 20 start_index: 40 end_index: 31
15	ExprRange	lambda_map: 20 start_index: 40 end_index: 41
16	ExprRange	lambda_map: 20 start_index: 29 end_index: 31
17	ExprTuple	21, 23
18	Literal
19	ExprTuple	22, 23
20	Lambda	parameter: 33 body: 24
21	Operation	operator: 34 operands: 25
22	Operation	operator: 34 operands: 26
23	Literal
24	Operation	operator: 27 operand: 33
25	ExprTuple	29, 30
26	ExprTuple	31, 32
27	Variable
28	ExprTuple	33
29	Operation	operator: 34 operands: 35
30	Operation	operator: 37 operand: 40
31	Variable
32	Operation	operator: 37 operand: 41
33	Variable
34	Literal
35	ExprTuple	41, 39
36	ExprTuple	40
37	Literal
38	ExprTuple	41
39	Literal
40	Variable
41	Variable