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 f_i_to_j
from proveit.logic import Equals
from proveit.numbers import Add, one

# build up the expression from sub-expressions
expr = Lambda([f, i, j], Conditional(Equals([f_i_to_j], []), Equals(Add(j, one), i)))

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) = () \textrm{ if } \left(j + 1\right) = i\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	19, 15, 16
2	Conditional	value: 3 condition: 4
3	Operation	operator: 6 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 15
8	ExprTuple	11
9	ExprTuple
10	Operation	operator: 12 operands: 13
11	ExprRange	lambda_map: 14 start_index: 15 end_index: 16
12	Literal
13	ExprTuple	16, 17
14	Lambda	parameter: 21 body: 18
15	Variable
16	Variable
17	Literal
18	Operation	operator: 19 operand: 21
19	Variable
20	ExprTuple	21
21	Variable