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

# build up the expression from sub-expressions
expr = Lambda([a, b], Conditional(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))]), And(InSet(a, Integer), InSet(b, 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, b\right) \mapsto \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) \textrm{ if } a \in \mathbb{Z} ,  b \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	parameters: 1 body: 2
1	ExprTuple	71, 73
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 19 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10
8	Lambda	parameters: 11 body: 12
9	Operation	operator: 28 operands: 13
10	Operation	operator: 28 operands: 14
11	ExprTuple	70, 68, 59, 60
12	Conditional	value: 15 condition: 16
13	ExprTuple	71, 17
14	ExprTuple	73, 17
15	Operation	operator: 31 operands: 18
16	Operation	operator: 19 operands: 20
17	Literal
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: 58 end_index: 34
27	ExprRange	lambda_map: 35 start_index: 36 end_index: 37
28	Literal
29	ExprTuple	38, 39
30	ExprTuple	40, 41
31	Literal
32	ExprTuple	42, 43
33	Lambda	parameter: 76 body: 44
34	Operation	operator: 74 operand: 68
35	Lambda	parameter: 76 body: 46
36	Operation	operator: 74 operand: 59
37	Operation	operator: 74 operand: 60
38	Operation	operator: 66 operands: 49
39	Literal
40	Operation	operator: 66 operands: 50
41	Operation	operator: 66 operands: 51
42	Operation	operator: 66 operands: 52
43	Operation	operator: 66 operands: 53
44	Operation	operator: 55 operand: 61
45	ExprTuple	68
46	Operation	operator: 55 operand: 62
47	ExprTuple	59
48	ExprTuple	60
49	ExprTuple	57, 58
50	ExprTuple	70, 71
51	ExprTuple	59, 73
52	ExprTuple	68, 71
53	ExprTuple	60, 73
54	ExprTuple	61
55	Variable
56	ExprTuple	62
57	Operation	operator: 66 operands: 63
58	Operation	operator: 74 operand: 70
59	Variable
60	Variable
61	Operation	operator: 66 operands: 65
62	Operation	operator: 66 operands: 67
63	ExprTuple	68, 69
64	ExprTuple	70
65	ExprTuple	72, 71
66	Literal
67	ExprTuple	72, 73
68	Variable
69	Literal
70	Variable
71	Variable
72	Operation	operator: 74 operand: 76
73	Variable
74	Literal
75	ExprTuple	76
76	Variable