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 merge_back_equiv
from proveit.logic import And, Equals, InSet
from proveit.numbers import Add, Natural, one, subtract

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([f, i, j, k], Conditional(merge_back_equiv, And(InSet(subtract(k, i), Natural), Equals(k, 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(\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(j\right), f\left(k\right)\right) =  \\ \left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(k\right)\right) \end{array} \end{array} \textrm{ if } \left(k - i\right) \in \mathbb{N} ,  k = \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	parameters: 2 body: 3
2	ExprTuple	29, 38, 33, 31
3	Conditional	value: 4 condition: 5
4	Operation	operator: 18 operands: 6
5	Operation	operator: 7 operands: 8
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12
9	ExprTuple	13, 14
10	ExprTuple	15
11	Operation	operator: 16 operands: 17
12	Operation	operator: 18 operands: 19
13	ExprRange	lambda_map: 21 start_index: 38 end_index: 33
14	Operation	operator: 29 operand: 31
15	ExprRange	lambda_map: 21 start_index: 38 end_index: 31
16	Literal
17	ExprTuple	22, 23
18	Literal
19	ExprTuple	31, 24
20	ExprTuple	31
21	Lambda	parameter: 35 body: 25
22	Operation	operator: 27 operands: 26
23	Literal
24	Operation	operator: 27 operands: 28
25	Operation	operator: 29 operand: 35
26	ExprTuple	31, 32
27	Literal
28	ExprTuple	33, 34
29	Variable
30	ExprTuple	35
31	Variable
32	Operation	operator: 36 operand: 38
33	Variable
34	Literal
35	Variable
36	Literal
37	ExprTuple	38
38	Variable