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 Equals, Forall, InSet
from proveit.numbers import Add, Integer, Natural, one, subtract

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [i, j, k, l], instance_expr = shift_equiv, conditions = [InSet(subtract(Add(j, one), i), Natural), Equals(k, subtract(i, a)), Equals(l, subtract(j, a))]), InSet(a, Integer))

# 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\{\forall_{i, j, k, l~|~\left(\left(j + 1\right) - i\right) \in \mathbb{N}, k = \left(i - a\right), l = \left(j - a\right)}~\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)\right) \textrm{ if } a \in \mathbb{Z}\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: 3 operand: 6
2	Operation	operator: 22 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	57, 7
6	Lambda	parameters: 8 body: 9
7	Literal
8	ExprTuple	55, 53, 31, 33
9	Conditional	value: 10 condition: 11
10	Operation	operator: 25 operands: 12
11	Operation	operator: 13 operands: 14
12	ExprTuple	15, 16
13	Literal
14	ExprTuple	17, 18, 19
15	ExprTuple	20
16	ExprTuple	21
17	Operation	operator: 22 operands: 23
18	Operation	operator: 25 operands: 24
19	Operation	operator: 25 operands: 26
20	ExprRange	lambda_map: 27 start_index: 55 end_index: 53
21	ExprRange	lambda_map: 28 start_index: 31 end_index: 33
22	Literal
23	ExprTuple	29, 30
24	ExprTuple	31, 32
25	Literal
26	ExprTuple	33, 34
27	Lambda	parameter: 56 body: 35
28	Lambda	parameter: 56 body: 36
29	Operation	operator: 51 operands: 37
30	Literal
31	Variable
32	Operation	operator: 51 operands: 38
33	Variable
34	Operation	operator: 51 operands: 39
35	Operation	operator: 41 operand: 56
36	Operation	operator: 41 operand: 46
37	ExprTuple	43, 44
38	ExprTuple	55, 45
39	ExprTuple	53, 45
40	ExprTuple	56
41	Variable
42	ExprTuple	46
43	Operation	operator: 51 operands: 47
44	Operation	operator: 49 operand: 55
45	Operation	operator: 49 operand: 57
46	Operation	operator: 51 operands: 52
47	ExprTuple	53, 54
48	ExprTuple	55
49	Literal
50	ExprTuple	57
51	Literal
52	ExprTuple	56, 57
53	Variable
54	Literal
55	Variable
56	Variable
57	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 ¶