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