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, m, n
from proveit.core_expr_types import Len
from proveit.core_expr_types.tuples import general_range_of_ranges
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Add, Natural, one, zero

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([m, n], Conditional(Forall(instance_param_or_params = [f, i, j], instance_expr = Equals(Len(operands = general_range_of_ranges), zero).with_wrapping_at(1)), And(InSet(m, Natural), InSet(n, Natural), 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(m, n\right) \mapsto \left\{\forall_{f, i, j}~\left(\begin{array}{c} \begin{array}{l} |\left(f\left(m, i\left(m\right)\right), f\left(m, i\left(m\right) + 1\right), \ldots, f\left(m, j\left(m\right)\right), f\left(m + 1, i\left(m + 1\right)\right), f\left(m + 1, i\left(m + 1\right) + 1\right), \ldots, f\left(m + 1, j\left(m + 1\right)\right), \ldots\ldots, f\left(n, i\left(n\right)\right), f\left(n, i\left(n\right) + 1\right), \ldots, f\left(n, j\left(n\right)\right)\right)| \\  = 0 \end{array} \end{array}\right) \textrm{ if } m \in \mathbb{N} ,  n \in \mathbb{N} ,  \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	33, 34
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 10
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	11, 12, 13
10	Lambda	parameters: 14 body: 15
11	Operation	operator: 17 operands: 16
12	Operation	operator: 17 operands: 18
13	Operation	operator: 20 operands: 19
14	ExprTuple	44, 41, 42
15	Operation	operator: 20 operands: 21
16	ExprTuple	33, 22
17	Literal
18	ExprTuple	34, 22
19	ExprTuple	23, 33
20	Literal
21	ExprTuple	24, 25
22	Literal
23	Operation	operator: 26 operands: 27
24	Operation	operator: 28 operands: 29
25	Literal
26	Literal
27	ExprTuple	34, 30
28	Literal
29	ExprTuple	31
30	Literal
31	ExprRange	lambda_map: 32 start_index: 33 end_index: 34
32	Lambda	parameter: 46 body: 35
33	Variable
34	Variable
35	ExprRange	lambda_map: 36 start_index: 37 end_index: 38
36	Lambda	parameter: 47 body: 40
37	Operation	operator: 41 operand: 46
38	Operation	operator: 42 operand: 46
39	ExprTuple	47
40	Operation	operator: 44 operands: 45
41	Variable
42	Variable
43	ExprTuple	46
44	Variable
45	ExprTuple	46, 47
46	Variable
47	Variable