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, four, one, three, two

# build up the expression from sub-expressions
sub_expr1 = Add(i, four)
expr = Lambda([f, i, j], Conditional(Equals([f_i_to_j], [Function(f, [i]), Function(f, [Add(i, one)]), Function(f, [Add(i, two)]), Function(f, [Add(i, three)]), 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), f\left(i + 3\right), f\left(i + 4\right)\right) \textrm{ if } j = \left(i + 4\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	28, 39, 17
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	17, 27
8	ExprTuple	10
9	ExprTuple	11, 12, 13, 14, 15
10	ExprRange	lambda_map: 16 start_index: 39 end_index: 17
11	Operation	operator: 28 operand: 39
12	Operation	operator: 28 operand: 24
13	Operation	operator: 28 operand: 25
14	Operation	operator: 28 operand: 26
15	Operation	operator: 28 operand: 27
16	Lambda	parameter: 35 body: 23
17	Variable
18	ExprTuple	39
19	ExprTuple	24
20	ExprTuple	25
21	ExprTuple	26
22	ExprTuple	27
23	Operation	operator: 28 operand: 35
24	Operation	operator: 33 operands: 30
25	Operation	operator: 33 operands: 31
26	Operation	operator: 33 operands: 32
27	Operation	operator: 33 operands: 34
28	Variable
29	ExprTuple	35
30	ExprTuple	39, 36
31	ExprTuple	39, 37
32	ExprTuple	39, 38
33	Literal
34	ExprTuple	39, 40
35	Variable
36	Literal
37	Literal
38	Literal
39	Variable
40	Literal