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 Lambda, a, f, 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(f, Forall(instance_param_or_params = [a], instance_expr = 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))]), domain = 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())

f \mapsto \left[\forall_{a \in \mathbb{Z}}~\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)\right]\right]

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 50 body: 2
1	ExprTuple	50
2	Operation	operator: 8 operand: 4
3	ExprTuple	4
4	Lambda	parameter: 67 body: 5
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operand: 11
7	Operation	operator: 27 operands: 10
8	Literal
9	ExprTuple	11
10	ExprTuple	67, 12
11	Lambda	parameters: 13 body: 14
12	Literal
13	ExprTuple	65, 63, 52, 53
14	Conditional	value: 15 condition: 16
15	Operation	operator: 30 operands: 17
16	Operation	operator: 18 operands: 19
17	ExprTuple	20, 21
18	Literal
19	ExprTuple	22, 23, 24
20	ExprTuple	25
21	ExprTuple	26
22	Operation	operator: 27 operands: 28
23	Operation	operator: 30 operands: 29
24	Operation	operator: 30 operands: 31
25	ExprRange	lambda_map: 32 start_index: 55 end_index: 33
26	ExprRange	lambda_map: 34 start_index: 35 end_index: 36
27	Literal
28	ExprTuple	37, 38
29	ExprTuple	52, 39
30	Literal
31	ExprTuple	53, 40
32	Lambda	parameter: 72 body: 41
33	Operation	operator: 69 operand: 63
34	Lambda	parameter: 72 body: 43
35	Operation	operator: 69 operand: 52
36	Operation	operator: 69 operand: 53
37	Operation	operator: 61 operands: 46
38	Literal
39	Operation	operator: 61 operands: 47
40	Operation	operator: 61 operands: 48
41	Operation	operator: 50 operand: 66
42	ExprTuple	63
43	Operation	operator: 50 operand: 57
44	ExprTuple	52
45	ExprTuple	53
46	ExprTuple	54, 55
47	ExprTuple	65, 56
48	ExprTuple	63, 56
49	ExprTuple	66
50	Variable
51	ExprTuple	57
52	Variable
53	Variable
54	Operation	operator: 61 operands: 58
55	Operation	operator: 69 operand: 65
56	Operation	operator: 69 operand: 67
57	Operation	operator: 61 operands: 62
58	ExprTuple	63, 64
59	ExprTuple	65
60	ExprTuple	67
61	Literal
62	ExprTuple	66, 67
63	Variable
64	Operation	operator: 69 operand: 71
65	Variable
66	Operation	operator: 69 operand: 72
67	Variable
68	ExprTuple	71
69	Literal
70	ExprTuple	72
71	Literal
72	Variable