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 Conditional, ExprTuple, 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 = ExprTuple(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())

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