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 shift_equiv
from proveit.logic import And, Equals, InSet
from proveit.numbers import Add, Natural, one, subtract

# build up the expression from sub-expressions
expr = Conditional(shift_equiv, And(InSet(subtract(Add(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: 46 end_index: 44
12	ExprRange	lambda_map: 19 start_index: 22 end_index: 24
13	Literal
14	ExprTuple	20, 21
15	ExprTuple	22, 23
16	Literal
17	ExprTuple	24, 25
18	Lambda	parameter: 47 body: 26
19	Lambda	parameter: 47 body: 27
20	Operation	operator: 42 operands: 28
21	Literal
22	Variable
23	Operation	operator: 42 operands: 29
24	Variable
25	Operation	operator: 42 operands: 30
26	Operation	operator: 32 operand: 47
27	Operation	operator: 32 operand: 37
28	ExprTuple	34, 35
29	ExprTuple	46, 36
30	ExprTuple	44, 36
31	ExprTuple	47
32	Variable
33	ExprTuple	37
34	Operation	operator: 42 operands: 38
35	Operation	operator: 40 operand: 46
36	Operation	operator: 40 operand: 48
37	Operation	operator: 42 operands: 43
38	ExprTuple	44, 45
39	ExprTuple	46
40	Literal
41	ExprTuple	48
42	Literal
43	ExprTuple	47, 48
44	Variable
45	Literal
46	Variable
47	Variable
48	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 ¶