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 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 = 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	67, 69
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	66, 64, 54, 55
12	Conditional	value: 15 condition: 16
13	ExprTuple	67, 17
14	ExprTuple	69, 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: 66 end_index: 64
27	ExprRange	lambda_map: 34 start_index: 54 end_index: 55
28	Literal
29	ExprTuple	35, 36
30	ExprTuple	37, 38
31	Literal
32	ExprTuple	39, 40
33	Lambda	parameter: 68 body: 41
34	Lambda	parameter: 68 body: 43
35	Operation	operator: 62 operands: 44
36	Literal
37	Operation	operator: 62 operands: 45
38	Operation	operator: 62 operands: 46
39	Operation	operator: 62 operands: 47
40	Operation	operator: 62 operands: 48
41	Operation	operator: 50 operand: 56
42	ExprTuple	68
43	Operation	operator: 50 operand: 57
44	ExprTuple	52, 53
45	ExprTuple	66, 67
46	ExprTuple	54, 69
47	ExprTuple	64, 67
48	ExprTuple	55, 69
49	ExprTuple	56
50	Variable
51	ExprTuple	57
52	Operation	operator: 62 operands: 58
53	Operation	operator: 59 operand: 66
54	Variable
55	Variable
56	Operation	operator: 62 operands: 61
57	Operation	operator: 62 operands: 63
58	ExprTuple	64, 65
59	Literal
60	ExprTuple	66
61	ExprTuple	68, 67
62	Literal
63	ExprTuple	68, 69
64	Variable
65	Literal
66	Variable
67	Variable
68	Variable
69	Variable