Expression of type Conditional ¶

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, 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 = 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\{\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	Conditional	value: 1 condition: 2
1	Operation	operator: 16 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	8, 9, 10
6	ExprTuple	11
7	ExprTuple	12
8	Operation	operator: 13 operands: 14
9	Operation	operator: 16 operands: 15
10	Operation	operator: 16 operands: 17
11	ExprRange	lambda_map: 18 start_index: 41 end_index: 19
12	ExprRange	lambda_map: 20 start_index: 21 end_index: 22
13	Literal
14	ExprTuple	23, 24
15	ExprTuple	38, 25
16	Literal
17	ExprTuple	39, 26
18	Lambda	parameter: 58 body: 27
19	Operation	operator: 55 operand: 49
20	Lambda	parameter: 58 body: 29
21	Operation	operator: 55 operand: 38
22	Operation	operator: 55 operand: 39
23	Operation	operator: 47 operands: 32
24	Literal
25	Operation	operator: 47 operands: 33
26	Operation	operator: 47 operands: 34
27	Operation	operator: 36 operand: 52
28	ExprTuple	49
29	Operation	operator: 36 operand: 43
30	ExprTuple	38
31	ExprTuple	39
32	ExprTuple	40, 41
33	ExprTuple	51, 42
34	ExprTuple	49, 42
35	ExprTuple	52
36	Variable
37	ExprTuple	43
38	Variable
39	Variable
40	Operation	operator: 47 operands: 44
41	Operation	operator: 55 operand: 51
42	Operation	operator: 55 operand: 53
43	Operation	operator: 47 operands: 48
44	ExprTuple	49, 50
45	ExprTuple	51
46	ExprTuple	53
47	Literal
48	ExprTuple	52, 53
49	Variable
50	Operation	operator: 55 operand: 57
51	Variable
52	Operation	operator: 55 operand: 58
53	Variable
54	ExprTuple	57
55	Literal
56	ExprTuple	58
57	Literal
58	Variable

Expression of type Conditional¶

from the theory of proveit.core_expr_types.tuples¶

Expression of type Conditional ¶

from the theory of proveit.core_expr_types.tuples ¶