Expression of type ExprTuple

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 ExprTuple, 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 = ExprTuple(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())

\left(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]\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 51 body: 3
2	ExprTuple	51
3	Operation	operator: 9 operand: 5
4	ExprTuple	5
5	Lambda	parameter: 68 body: 6
6	Conditional	value: 7 condition: 8
7	Operation	operator: 9 operand: 12
8	Operation	operator: 28 operands: 11
9	Literal
10	ExprTuple	12
11	ExprTuple	68, 13
12	Lambda	parameters: 14 body: 15
13	Literal
14	ExprTuple	66, 64, 53, 54
15	Conditional	value: 16 condition: 17
16	Operation	operator: 31 operands: 18
17	Operation	operator: 19 operands: 20
18	ExprTuple	21, 22
19	Literal
20	ExprTuple	23, 24, 25
21	ExprTuple	26
22	ExprTuple	27
23	Operation	operator: 28 operands: 29
24	Operation	operator: 31 operands: 30
25	Operation	operator: 31 operands: 32
26	ExprRange	lambda_map: 33 start_index: 56 end_index: 34
27	ExprRange	lambda_map: 35 start_index: 36 end_index: 37
28	Literal
29	ExprTuple	38, 39
30	ExprTuple	53, 40
31	Literal
32	ExprTuple	54, 41
33	Lambda	parameter: 73 body: 42
34	Operation	operator: 70 operand: 64
35	Lambda	parameter: 73 body: 44
36	Operation	operator: 70 operand: 53
37	Operation	operator: 70 operand: 54
38	Operation	operator: 62 operands: 47
39	Literal
40	Operation	operator: 62 operands: 48
41	Operation	operator: 62 operands: 49
42	Operation	operator: 51 operand: 67
43	ExprTuple	64
44	Operation	operator: 51 operand: 58
45	ExprTuple	53
46	ExprTuple	54
47	ExprTuple	55, 56
48	ExprTuple	66, 57
49	ExprTuple	64, 57
50	ExprTuple	67
51	Variable
52	ExprTuple	58
53	Variable
54	Variable
55	Operation	operator: 62 operands: 59
56	Operation	operator: 70 operand: 66
57	Operation	operator: 70 operand: 68
58	Operation	operator: 62 operands: 63
59	ExprTuple	64, 65
60	ExprTuple	66
61	ExprTuple	68
62	Literal
63	ExprTuple	67, 68
64	Variable
65	Operation	operator: 70 operand: 72
66	Variable
67	Operation	operator: 70 operand: 73
68	Variable
69	ExprTuple	72
70	Literal
71	ExprTuple	73
72	Literal
73	Variable