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 Lambda, f, i, j
from proveit.core_expr_types import Len
from proveit.core_expr_types.tuples import general_range_of_ranges
from proveit.logic import Equals
from proveit.numbers import zero

# build up the expression from sub-expressions
expr = Lambda([f, i, j], Equals(Len(operands = general_range_of_ranges), zero).with_wrapping_at(1))

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(f, i, j\right) \mapsto \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)

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	22, 19, 20
2	Operation	operator: 3 operands: 4
3	Literal
4	ExprTuple	5, 6
5	Operation	operator: 7 operands: 8
6	Literal
7	Literal
8	ExprTuple	9
9	ExprRange	lambda_map: 10 start_index: 11 end_index: 12
10	Lambda	parameter: 24 body: 13
11	Variable
12	Variable
13	ExprRange	lambda_map: 14 start_index: 15 end_index: 16
14	Lambda	parameter: 25 body: 18
15	Operation	operator: 19 operand: 24
16	Operation	operator: 20 operand: 24
17	ExprTuple	25
18	Operation	operator: 22 operands: 23
19	Variable
20	Variable
21	ExprTuple	24
22	Variable
23	ExprTuple	24, 25
24	Variable
25	Variable