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, i_to_j_len
from proveit.logic import InSet
from proveit.numbers import Natural

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