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

# build up the expression from sub-expressions
expr = Lambda([i, j, k, l], Conditional(neg_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)))))

# 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()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Lambda	parameters: 1 body: 2
1	ExprTuple	57, 55, 46, 47
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: 45 end_index: 21
14	ExprRange	lambda_map: 22 start_index: 23 end_index: 24
15	Literal
16	ExprTuple	25, 26
17	ExprTuple	27, 28
18	Literal
19	ExprTuple	29, 30
20	Lambda	parameter: 63 body: 31
21	Operation	operator: 61 operand: 55
22	Lambda	parameter: 63 body: 33
23	Operation	operator: 61 operand: 46
24	Operation	operator: 61 operand: 47
25	Operation	operator: 53 operands: 36
26	Literal
27	Operation	operator: 53 operands: 37
28	Operation	operator: 53 operands: 38
29	Operation	operator: 53 operands: 39
30	Operation	operator: 53 operands: 40
31	Operation	operator: 42 operand: 48
32	ExprTuple	55
33	Operation	operator: 42 operand: 49
34	ExprTuple	46
35	ExprTuple	47
36	ExprTuple	44, 45
37	ExprTuple	57, 58
38	ExprTuple	46, 60
39	ExprTuple	55, 58
40	ExprTuple	47, 60
41	ExprTuple	48
42	Variable
43	ExprTuple	49
44	Operation	operator: 53 operands: 50
45	Operation	operator: 61 operand: 57
46	Variable
47	Variable
48	Operation	operator: 53 operands: 52
49	Operation	operator: 53 operands: 54
50	ExprTuple	55, 56
51	ExprTuple	57
52	ExprTuple	59, 58
53	Literal
54	ExprTuple	59, 60
55	Variable
56	Literal
57	Variable
58	Variable
59	Operation	operator: 61 operand: 63
60	Variable
61	Literal
62	ExprTuple	63
63	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 ¶