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, i_to_j_len, range_i_to_j
from proveit.logic import Equals, InSet
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([f, i, j], Conditional(Equals(Len(operands = [f_i_to_j]), Len(operands = [range_i_to_j])), InSet(i_to_j_len, 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\{|\left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j\right)\right)| = |\left(i, \left(i + 1\right), \ldots, j\right)| \textrm{ if } \left(j - i + 1\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	30, 29, 25
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: 15 operands: 14
11	Operation	operator: 15 operands: 16
12	Operation	operator: 17 operands: 18
13	Literal
14	ExprTuple	19
15	Literal
16	ExprTuple	20
17	Literal
18	ExprTuple	25, 21, 22
19	ExprRange	lambda_map: 23 start_index: 29 end_index: 25
20	ExprRange	lambda_map: 24 start_index: 29 end_index: 25
21	Operation	operator: 26 operand: 29
22	Literal
23	Lambda	parameter: 32 body: 28
24	Lambda	parameter: 32 body: 32
25	Variable
26	Literal
27	ExprTuple	29
28	Operation	operator: 30 operand: 32
29	Variable
30	Variable
31	ExprTuple	32
32	Variable