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, i, j, x
from proveit.core_expr_types import Len, f_i_to_j
from proveit.logic import Equals, InSet
from proveit.numbers import Add, Natural, Neg, two

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([i, j], Conditional(Equals(Len(operands = [f_i_to_j, x]), Add(j, Neg(i), two)), 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(i, j\right) \mapsto \left\{|\left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j\right), x\right)| = \left(j - i + 2\right) \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	27, 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	Operation	operator: 17 operands: 14
11	Operation	operator: 15 operands: 16
12	Operation	operator: 17 operands: 18
13	Literal
14	ExprTuple	22, 19
15	Literal
16	ExprTuple	26, 20, 21
17	Literal
18	ExprTuple	22
19	Variable
20	Operation	operator: 23 operand: 27
21	Literal
22	ExprRange	lambda_map: 25 start_index: 27 end_index: 26
23	Literal
24	ExprTuple	27
25	Lambda	parameter: 31 body: 28
26	Variable
27	Variable
28	Operation	operator: 29 operand: 31
29	Variable
30	ExprTuple	31
31	Variable