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
from proveit.core_expr_types import Len, f_i_to_j, iter_ext_equiv
from proveit.logic import InSet
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([f, i, j], Conditional(iter_ext_equiv, InSet(Len(operands = [f_i_to_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\right) \mapsto \left\{\begin{array}{c} \begin{array}{l} \left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j + 1\right)\right) =  \\ \left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j\right), f\left(j + 1\right)\right) \end{array} \end{array} \textrm{ if } |\left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j\right)\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	28, 22, 26
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	19, 15
12	Operation	operator: 16 operands: 17
13	Literal
14	ExprRange	lambda_map: 21 start_index: 22 end_index: 20
15	Operation	operator: 28 operand: 20
16	Literal
17	ExprTuple	19
18	ExprTuple	20
19	ExprRange	lambda_map: 21 start_index: 22 end_index: 26
20	Operation	operator: 23 operands: 24
21	Lambda	parameter: 30 body: 25
22	Variable
23	Literal
24	ExprTuple	26, 27
25	Operation	operator: 28 operand: 30
26	Variable
27	Literal
28	Variable
29	ExprTuple	30
30	Variable