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 partition_front_equiv
from proveit.logic import InSet
from proveit.numbers import Natural, subtract

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([f, i, j], Conditional(partition_front_equiv, InSet(subtract(j, i), 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\right)\right) =  \\ \left(f\left(i\right),f\left(i + 1\right), f\left(i + 2\right), \ldots, f\left(j\right)\right) \end{array} \end{array} \textrm{ if } \left(j - i\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, 30, 20
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: 23 operands: 17
13	Literal
14	ExprRange	lambda_map: 18 start_index: 30 end_index: 20
15	Operation	operator: 27 operand: 30
16	ExprRange	lambda_map: 18 start_index: 19 end_index: 20
17	ExprTuple	20, 21
18	Lambda	parameter: 31 body: 22
19	Operation	operator: 23 operands: 24
20	Variable
21	Operation	operator: 25 operand: 30
22	Operation	operator: 27 operand: 31
23	Literal
24	ExprTuple	30, 29
25	Literal
26	ExprTuple	30
27	Variable
28	ExprTuple	31
29	Literal
30	Variable
31	Variable