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, i, j, k, l
from proveit.core_expr_types.tuples import neg_shift_equiv
from proveit.logic import And, Equals, InSet
from proveit.numbers import Natural, one, subtract

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

# 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\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) \textrm{ if } \left(\left(j - 1\right) - i\right) \in \mathbb{N} ,  k = \left(i - a\right) ,  l = \left(j - a\right)\right..

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Lambda	parameters: 1 body: 2
1	ExprTuple	53, 51, 40, 41
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: 43 end_index: 21
14	ExprRange	lambda_map: 22 start_index: 23 end_index: 24
15	Literal
16	ExprTuple	25, 26
17	ExprTuple	40, 27
18	Literal
19	ExprTuple	41, 28
20	Lambda	parameter: 60 body: 29
21	Operation	operator: 57 operand: 51
22	Lambda	parameter: 60 body: 31
23	Operation	operator: 57 operand: 40
24	Operation	operator: 57 operand: 41
25	Operation	operator: 49 operands: 34
26	Literal
27	Operation	operator: 49 operands: 35
28	Operation	operator: 49 operands: 36
29	Operation	operator: 38 operand: 54
30	ExprTuple	51
31	Operation	operator: 38 operand: 45
32	ExprTuple	40
33	ExprTuple	41
34	ExprTuple	42, 43
35	ExprTuple	53, 44
36	ExprTuple	51, 44
37	ExprTuple	54
38	Variable
39	ExprTuple	45
40	Variable
41	Variable
42	Operation	operator: 49 operands: 46
43	Operation	operator: 57 operand: 53
44	Operation	operator: 57 operand: 55
45	Operation	operator: 49 operands: 50
46	ExprTuple	51, 52
47	ExprTuple	53
48	ExprTuple	55
49	Literal
50	ExprTuple	54, 55
51	Variable
52	Operation	operator: 57 operand: 59
53	Variable
54	Operation	operator: 57 operand: 60
55	Variable
56	ExprTuple	59
57	Literal
58	ExprTuple	60
59	Literal
60	Variable

Expression of type Lambda¶

from the theory of proveit.core_expr_types.tuples¶

Expression of type Lambda ¶

from the theory of proveit.core_expr_types.tuples ¶