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
from proveit.core_expr_types import Len, f_i_to_j, iter_ext_equiv
from proveit.logic import InSet
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = Lambda([f, i, j], Conditional(iter_ext_equiv, InSet(Len(operands = [f_i_to_j]), 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(f, i, j\right) \mapsto \left\{\begin{array}{c} \begin{array}{l} \left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j + 1\right)\right) =  \\ \left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j\right), f\left(j + 1\right)\right) \end{array} \end{array} \textrm{ if } |\left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j\right)\right)| \in \mathbb{N}\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	27, 21, 25
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12
9	ExprTuple	13
10	ExprTuple	18, 14
11	Operation	operator: 15 operands: 16
12	Literal
13	ExprRange	lambda_map: 20 start_index: 21 end_index: 19
14	Operation	operator: 27 operand: 19
15	Literal
16	ExprTuple	18
17	ExprTuple	19
18	ExprRange	lambda_map: 20 start_index: 21 end_index: 25
19	Operation	operator: 22 operands: 23
20	Lambda	parameter: 29 body: 24
21	Variable
22	Literal
23	ExprTuple	25, 26
24	Operation	operator: 27 operand: 29
25	Variable
26	Literal
27	Variable
28	ExprTuple	29
29	Variable