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, 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 = 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())

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]

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 59 body: 2
1	ExprTuple	59
2	Operation	operator: 9 operand: 4
3	ExprTuple	4
4	Lambda	parameters: 5 body: 6
5	ExprTuple	75, 77
6	Conditional	value: 7 condition: 8
7	Operation	operator: 9 operand: 12
8	Operation	operator: 23 operands: 11
9	Literal
10	ExprTuple	12
11	ExprTuple	13, 14
12	Lambda	parameters: 15 body: 16
13	Operation	operator: 32 operands: 17
14	Operation	operator: 32 operands: 18
15	ExprTuple	74, 72, 63, 64
16	Conditional	value: 19 condition: 20
17	ExprTuple	75, 21
18	ExprTuple	77, 21
19	Operation	operator: 35 operands: 22
20	Operation	operator: 23 operands: 24
21	Literal
22	ExprTuple	25, 26
23	Literal
24	ExprTuple	27, 28, 29
25	ExprTuple	30
26	ExprTuple	31
27	Operation	operator: 32 operands: 33
28	Operation	operator: 35 operands: 34
29	Operation	operator: 35 operands: 36
30	ExprRange	lambda_map: 37 start_index: 62 end_index: 38
31	ExprRange	lambda_map: 39 start_index: 40 end_index: 41
32	Literal
33	ExprTuple	42, 43
34	ExprTuple	44, 45
35	Literal
36	ExprTuple	46, 47
37	Lambda	parameter: 80 body: 48
38	Operation	operator: 78 operand: 72
39	Lambda	parameter: 80 body: 50
40	Operation	operator: 78 operand: 63
41	Operation	operator: 78 operand: 64
42	Operation	operator: 70 operands: 53
43	Literal
44	Operation	operator: 70 operands: 54
45	Operation	operator: 70 operands: 55
46	Operation	operator: 70 operands: 56
47	Operation	operator: 70 operands: 57
48	Operation	operator: 59 operand: 65
49	ExprTuple	72
50	Operation	operator: 59 operand: 66
51	ExprTuple	63
52	ExprTuple	64
53	ExprTuple	61, 62
54	ExprTuple	74, 75
55	ExprTuple	63, 77
56	ExprTuple	72, 75
57	ExprTuple	64, 77
58	ExprTuple	65
59	Variable
60	ExprTuple	66
61	Operation	operator: 70 operands: 67
62	Operation	operator: 78 operand: 74
63	Variable
64	Variable
65	Operation	operator: 70 operands: 69
66	Operation	operator: 70 operands: 71
67	ExprTuple	72, 73
68	ExprTuple	74
69	ExprTuple	76, 75
70	Literal
71	ExprTuple	76, 77
72	Variable
73	Literal
74	Variable
75	Variable
76	Operation	operator: 78 operand: 80
77	Variable
78	Literal
79	ExprTuple	80
80	Variable