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 neg_shift_equiv
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Integer, Natural, one, subtract

# build up the expression from sub-expressions
expr = Lambda(a, Conditional(Forall(instance_param_or_params = [i, j, k, l], instance_expr = neg_shift_equiv, conditions = [InSet(subtract(subtract(j, one), i), Natural), Equals(k, subtract(i, a)), Equals(l, subtract(j, a))]), InSet(a, Integer)))

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())

a \mapsto \left\{\forall_{i, j, k, l~|~\left(\left(j - 1\right) - i\right) \in \mathbb{N}, k = \left(i - a\right), l = \left(j - a\right)}~\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)\right) \textrm{ if } a \in \mathbb{Z}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 63 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operand: 7
3	Operation	operator: 23 operands: 6
4	Literal
5	ExprTuple	7
6	ExprTuple	63, 8
7	Lambda	parameters: 9 body: 10
8	Literal
9	ExprTuple	61, 59, 48, 49
10	Conditional	value: 11 condition: 12
11	Operation	operator: 26 operands: 13
12	Operation	operator: 14 operands: 15
13	ExprTuple	16, 17
14	Literal
15	ExprTuple	18, 19, 20
16	ExprTuple	21
17	ExprTuple	22
18	Operation	operator: 23 operands: 24
19	Operation	operator: 26 operands: 25
20	Operation	operator: 26 operands: 27
21	ExprRange	lambda_map: 28 start_index: 51 end_index: 29
22	ExprRange	lambda_map: 30 start_index: 31 end_index: 32
23	Literal
24	ExprTuple	33, 34
25	ExprTuple	48, 35
26	Literal
27	ExprTuple	49, 36
28	Lambda	parameter: 68 body: 37
29	Operation	operator: 65 operand: 59
30	Lambda	parameter: 68 body: 39
31	Operation	operator: 65 operand: 48
32	Operation	operator: 65 operand: 49
33	Operation	operator: 57 operands: 42
34	Literal
35	Operation	operator: 57 operands: 43
36	Operation	operator: 57 operands: 44
37	Operation	operator: 46 operand: 62
38	ExprTuple	59
39	Operation	operator: 46 operand: 53
40	ExprTuple	48
41	ExprTuple	49
42	ExprTuple	50, 51
43	ExprTuple	61, 52
44	ExprTuple	59, 52
45	ExprTuple	62
46	Variable
47	ExprTuple	53
48	Variable
49	Variable
50	Operation	operator: 57 operands: 54
51	Operation	operator: 65 operand: 61
52	Operation	operator: 65 operand: 63
53	Operation	operator: 57 operands: 58
54	ExprTuple	59, 60
55	ExprTuple	61
56	ExprTuple	63
57	Literal
58	ExprTuple	62, 63
59	Variable
60	Operation	operator: 65 operand: 67
61	Variable
62	Operation	operator: 65 operand: 68
63	Variable
64	ExprTuple	67
65	Literal
66	ExprTuple	68
67	Literal
68	Variable