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, a, i, j, k, l
from proveit.core_expr_types.tuples import shift_equiv
from proveit.logic import And, Equals, InSet
from proveit.numbers import Add, Natural, one, subtract

# build up the expression from sub-expressions
expr = Lambda([i, j, k, l], Conditional(shift_equiv, And(InSet(subtract(Add(j, one), i), Natural), Equals(k, subtract(i, a)), Equals(l, subtract(j, a)))))

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(i, j, k, l\right) \mapsto \left\{\left(f\left(i\right), f\left(i + 1\right), \ldots, f\left(j\right)\right) = \left(f\left(k + a\right), f\left(\left(k + 1\right) + a\right), \ldots, f\left(l + a\right)\right) \textrm{ if } \left(\left(j + 1\right) - i\right) \in \mathbb{N} ,  k = \left(i - a\right) ,  l = \left(j - a\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	48, 46, 24, 26
2	Conditional	value: 3 condition: 4
3	Operation	operator: 18 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 11, 12
8	ExprTuple	13
9	ExprTuple	14
10	Operation	operator: 15 operands: 16
11	Operation	operator: 18 operands: 17
12	Operation	operator: 18 operands: 19
13	ExprRange	lambda_map: 20 start_index: 48 end_index: 46
14	ExprRange	lambda_map: 21 start_index: 24 end_index: 26
15	Literal
16	ExprTuple	22, 23
17	ExprTuple	24, 25
18	Literal
19	ExprTuple	26, 27
20	Lambda	parameter: 49 body: 28
21	Lambda	parameter: 49 body: 29
22	Operation	operator: 44 operands: 30
23	Literal
24	Variable
25	Operation	operator: 44 operands: 31
26	Variable
27	Operation	operator: 44 operands: 32
28	Operation	operator: 34 operand: 49
29	Operation	operator: 34 operand: 39
30	ExprTuple	36, 37
31	ExprTuple	48, 38
32	ExprTuple	46, 38
33	ExprTuple	49
34	Variable
35	ExprTuple	39
36	Operation	operator: 44 operands: 40
37	Operation	operator: 42 operand: 48
38	Operation	operator: 42 operand: 50
39	Operation	operator: 44 operands: 45
40	ExprTuple	46, 47
41	ExprTuple	48
42	Literal
43	ExprTuple	50
44	Literal
45	ExprTuple	49, 50
46	Variable
47	Literal
48	Variable
49	Variable
50	Variable