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, eight, five, four, one, seven, six, three, two

# build up the expression from sub-expressions
sub_expr1 = Add(i, eight)
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, [Add(i, four)]), Function(f, [Add(i, five)]), Function(f, [Add(i, six)]), Function(f, [Add(i, seven)]), 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), f\left(i + 5\right), f\left(i + 6\right), f\left(i + 7\right), f\left(i + 8\right)\right) \textrm{ if } j = \left(i + 8\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	40, 59, 21
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	21, 39
8	ExprTuple	10
9	ExprTuple	11, 12, 13, 14, 15, 16, 17, 18, 19
10	ExprRange	lambda_map: 20 start_index: 59 end_index: 21
11	Operation	operator: 40 operand: 59
12	Operation	operator: 40 operand: 32
13	Operation	operator: 40 operand: 33
14	Operation	operator: 40 operand: 34
15	Operation	operator: 40 operand: 35
16	Operation	operator: 40 operand: 36
17	Operation	operator: 40 operand: 37
18	Operation	operator: 40 operand: 38
19	Operation	operator: 40 operand: 39
20	Lambda	parameter: 51 body: 31
21	Variable
22	ExprTuple	59
23	ExprTuple	32
24	ExprTuple	33
25	ExprTuple	34
26	ExprTuple	35
27	ExprTuple	36
28	ExprTuple	37
29	ExprTuple	38
30	ExprTuple	39
31	Operation	operator: 40 operand: 51
32	Operation	operator: 49 operands: 42
33	Operation	operator: 49 operands: 43
34	Operation	operator: 49 operands: 44
35	Operation	operator: 49 operands: 45
36	Operation	operator: 49 operands: 46
37	Operation	operator: 49 operands: 47
38	Operation	operator: 49 operands: 48
39	Operation	operator: 49 operands: 50
40	Variable
41	ExprTuple	51
42	ExprTuple	59, 52
43	ExprTuple	59, 53
44	ExprTuple	59, 54
45	ExprTuple	59, 55
46	ExprTuple	59, 56
47	ExprTuple	59, 57
48	ExprTuple	59, 58
49	Literal
50	ExprTuple	59, 60
51	Variable
52	Literal
53	Literal
54	Literal
55	Literal
56	Literal
57	Literal
58	Literal
59	Variable
60	Literal