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, ExprRange, ExprTuple, Function, Lambda, Variable, f, i, j, m, n
from proveit.logic import Equals
from proveit.numbers import Add, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_b", latex_format = r"{_{-}b}")
sub_expr2 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Lambda([f, i, j, m, n], Conditional(Equals([ExprRange(sub_expr1, ExprRange(sub_expr2, Function(f, [sub_expr1, sub_expr2]), i, j), m, n)], []), Equals(Add(n, one), m))))

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, m, n\right) \mapsto \left\{\left(f\left(m, i\right), f\left(m, i + 1\right), \ldots, f\left(m, j\right), f\left(m + 1, i\right), f\left(m + 1, i + 1\right), \ldots, f\left(m + 1, j\right), \ldots\ldots, f\left(n, i\right), f\left(n, i + 1\right), \ldots, f\left(n, j\right)\right) = () \textrm{ if } \left(n + 1\right) = m\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	26, 22, 23, 16, 17
3	Conditional	value: 4 condition: 5
4	Operation	operator: 7 operands: 6
5	Operation	operator: 7 operands: 8
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 16
9	ExprTuple	12
10	ExprTuple
11	Operation	operator: 13 operands: 14
12	ExprRange	lambda_map: 15 start_index: 16 end_index: 17
13	Literal
14	ExprTuple	17, 18
15	Lambda	parameter: 28 body: 20
16	Variable
17	Variable
18	Literal
19	ExprTuple	28
20	ExprRange	lambda_map: 21 start_index: 22 end_index: 23
21	Lambda	parameter: 29 body: 25
22	Variable
23	Variable
24	ExprTuple	29
25	Operation	operator: 26 operands: 27
26	Variable
27	ExprTuple	28, 29
28	Variable
29	Variable