Expression of type Lambda

from the theory of proveit.numbers.numerals.decimals

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, Function, 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, two

# build up the expression from sub-expressions
sub_expr1 = Add(i, two)
expr = Lambda([f, i, j], Conditional(Equals([f_i_to_j], [Function(f, [i]), Function(f, [Add(i, one)]), Function(f, [sub_expr1])]), Equals(j, sub_expr1)))

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) = \left(f\left(i\right), f\left(i + 1\right), f\left(i + 2\right)\right) \textrm{ if } j = \left(i + 2\right)\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, 29, 15
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	15, 21
8	ExprTuple	10
9	ExprTuple	11, 12, 13
10	ExprRange	lambda_map: 14 start_index: 29 end_index: 15
11	Operation	operator: 22 operand: 29
12	Operation	operator: 22 operand: 20
13	Operation	operator: 22 operand: 21
14	Lambda	parameter: 27 body: 19
15	Variable
16	ExprTuple	29
17	ExprTuple	20
18	ExprTuple	21
19	Operation	operator: 22 operand: 27
20	Operation	operator: 25 operands: 24
21	Operation	operator: 25 operands: 26
22	Variable
23	ExprTuple	27
24	ExprTuple	29, 28
25	Literal
26	ExprTuple	29, 30
27	Variable
28	Literal
29	Variable
30	Literal