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, InSet
from proveit.numbers import Add, Natural, one, subtract

# build up the expression from sub-expressions
expr = Lambda([i, j, k, l], Conditional(shift_equiv_both, And(InSet(subtract(Add(j, one), i), Natural), Equals(Add(i, a), Add(k, b)), Equals(Add(j, a), Add(l, b)))))

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(i, j, k, l\right) \mapsto \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) \textrm{ if } \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)\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	53, 51, 41, 42
2	Conditional	value: 3 condition: 4
3	Operation	operator: 18 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 11, 12
8	ExprTuple	13
9	ExprTuple	14
10	Operation	operator: 15 operands: 16
11	Operation	operator: 18 operands: 17
12	Operation	operator: 18 operands: 19
13	ExprRange	lambda_map: 20 start_index: 53 end_index: 51
14	ExprRange	lambda_map: 21 start_index: 41 end_index: 42
15	Literal
16	ExprTuple	22, 23
17	ExprTuple	24, 25
18	Literal
19	ExprTuple	26, 27
20	Lambda	parameter: 55 body: 28
21	Lambda	parameter: 55 body: 30
22	Operation	operator: 49 operands: 31
23	Literal
24	Operation	operator: 49 operands: 32
25	Operation	operator: 49 operands: 33
26	Operation	operator: 49 operands: 34
27	Operation	operator: 49 operands: 35
28	Operation	operator: 37 operand: 43
29	ExprTuple	55
30	Operation	operator: 37 operand: 44
31	ExprTuple	39, 40
32	ExprTuple	53, 54
33	ExprTuple	41, 56
34	ExprTuple	51, 54
35	ExprTuple	42, 56
36	ExprTuple	43
37	Variable
38	ExprTuple	44
39	Operation	operator: 49 operands: 45
40	Operation	operator: 46 operand: 53
41	Variable
42	Variable
43	Operation	operator: 49 operands: 48
44	Operation	operator: 49 operands: 50
45	ExprTuple	51, 52
46	Literal
47	ExprTuple	53
48	ExprTuple	55, 54
49	Literal
50	ExprTuple	55, 56
51	Variable
52	Literal
53	Variable
54	Variable
55	Variable
56	Variable