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, five, four, one, three, two

# build up the expression from sub-expressions
sub_expr1 = Add(i, five)
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, [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)\right) \textrm{ if } j = \left(i + 5\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	31, 44, 18
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	18, 30
8	ExprTuple	10
9	ExprTuple	11, 12, 13, 14, 15, 16
10	ExprRange	lambda_map: 17 start_index: 44 end_index: 18
11	Operation	operator: 31 operand: 44
12	Operation	operator: 31 operand: 26
13	Operation	operator: 31 operand: 27
14	Operation	operator: 31 operand: 28
15	Operation	operator: 31 operand: 29
16	Operation	operator: 31 operand: 30
17	Lambda	parameter: 39 body: 25
18	Variable
19	ExprTuple	44
20	ExprTuple	26
21	ExprTuple	27
22	ExprTuple	28
23	ExprTuple	29
24	ExprTuple	30
25	Operation	operator: 31 operand: 39
26	Operation	operator: 37 operands: 33
27	Operation	operator: 37 operands: 34
28	Operation	operator: 37 operands: 35
29	Operation	operator: 37 operands: 36
30	Operation	operator: 37 operands: 38
31	Variable
32	ExprTuple	39
33	ExprTuple	44, 40
34	ExprTuple	44, 41
35	ExprTuple	44, 42
36	ExprTuple	44, 43
37	Literal
38	ExprTuple	44, 45
39	Variable
40	Literal
41	Literal
42	Literal
43	Literal
44	Variable
45	Literal