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, b, f, i, j, k, l
from proveit.core_expr_types.tuples import neg_shift_equiv_both
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Add, Integer, Natural, one, subtract

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(f, Forall(instance_param_or_params = [a, b], instance_expr = Forall(instance_param_or_params = [i, j, k, l], instance_expr = neg_shift_equiv_both, conditions = [InSet(subtract(Add(j, one), i), Natural), Equals(Add(i, a), Add(k, b)), Equals(Add(j, a), Add(l, b))]), 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, b \in \mathbb{Z}}~\left[\forall_{i, j, k, l~|~\left(\left(j + 1\right) - i\right) \in \mathbb{N}, \left(i + a\right) = \left(k + b\right), \left(j + a\right) = \left(l + b\right)}~\left(\left(f\left(i + a\right), f\left(\left(i - 1\right) + a\right), \ldots, f\left(j + a\right)\right) = \left(f\left(k + b\right), f\left(\left(k - 1\right) + b\right), \ldots, f\left(l + b\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: 60 body: 3
2	ExprTuple	60
3	Operation	operator: 10 operand: 5
4	ExprTuple	5
5	Lambda	parameters: 6 body: 7
6	ExprTuple	76, 78
7	Conditional	value: 8 condition: 9
8	Operation	operator: 10 operand: 13
9	Operation	operator: 24 operands: 12
10	Literal
11	ExprTuple	13
12	ExprTuple	14, 15
13	Lambda	parameters: 16 body: 17
14	Operation	operator: 33 operands: 18
15	Operation	operator: 33 operands: 19
16	ExprTuple	75, 73, 64, 65
17	Conditional	value: 20 condition: 21
18	ExprTuple	76, 22
19	ExprTuple	78, 22
20	Operation	operator: 36 operands: 23
21	Operation	operator: 24 operands: 25
22	Literal
23	ExprTuple	26, 27
24	Literal
25	ExprTuple	28, 29, 30
26	ExprTuple	31
27	ExprTuple	32
28	Operation	operator: 33 operands: 34
29	Operation	operator: 36 operands: 35
30	Operation	operator: 36 operands: 37
31	ExprRange	lambda_map: 38 start_index: 63 end_index: 39
32	ExprRange	lambda_map: 40 start_index: 41 end_index: 42
33	Literal
34	ExprTuple	43, 44
35	ExprTuple	45, 46
36	Literal
37	ExprTuple	47, 48
38	Lambda	parameter: 81 body: 49
39	Operation	operator: 79 operand: 73
40	Lambda	parameter: 81 body: 51
41	Operation	operator: 79 operand: 64
42	Operation	operator: 79 operand: 65
43	Operation	operator: 71 operands: 54
44	Literal
45	Operation	operator: 71 operands: 55
46	Operation	operator: 71 operands: 56
47	Operation	operator: 71 operands: 57
48	Operation	operator: 71 operands: 58
49	Operation	operator: 60 operand: 66
50	ExprTuple	73
51	Operation	operator: 60 operand: 67
52	ExprTuple	64
53	ExprTuple	65
54	ExprTuple	62, 63
55	ExprTuple	75, 76
56	ExprTuple	64, 78
57	ExprTuple	73, 76
58	ExprTuple	65, 78
59	ExprTuple	66
60	Variable
61	ExprTuple	67
62	Operation	operator: 71 operands: 68
63	Operation	operator: 79 operand: 75
64	Variable
65	Variable
66	Operation	operator: 71 operands: 70
67	Operation	operator: 71 operands: 72
68	ExprTuple	73, 74
69	ExprTuple	75
70	ExprTuple	77, 76
71	Literal
72	ExprTuple	77, 78
73	Variable
74	Literal
75	Variable
76	Variable
77	Operation	operator: 79 operand: 81
78	Variable
79	Literal
80	ExprTuple	81
81	Variable