Expression of type Lambda

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, 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 = 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(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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	32, 33
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	10, 11, 12
9	Lambda	parameters: 13 body: 14
10	Operation	operator: 16 operands: 15
11	Operation	operator: 16 operands: 17
12	Operation	operator: 19 operands: 18
13	ExprTuple	43, 40, 41
14	Operation	operator: 19 operands: 20
15	ExprTuple	32, 21
16	Literal
17	ExprTuple	33, 21
18	ExprTuple	22, 32
19	Literal
20	ExprTuple	23, 24
21	Literal
22	Operation	operator: 25 operands: 26
23	Operation	operator: 27 operands: 28
24	Literal
25	Literal
26	ExprTuple	33, 29
27	Literal
28	ExprTuple	30
29	Literal
30	ExprRange	lambda_map: 31 start_index: 32 end_index: 33
31	Lambda	parameter: 45 body: 34
32	Variable
33	Variable
34	ExprRange	lambda_map: 35 start_index: 36 end_index: 37
35	Lambda	parameter: 46 body: 39
36	Operation	operator: 40 operand: 45
37	Operation	operator: 41 operand: 45
38	ExprTuple	46
39	Operation	operator: 43 operands: 44
40	Variable
41	Variable
42	ExprTuple	45
43	Variable
44	ExprTuple	45, 46
45	Variable
46	Variable