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 shift_equiv_both
from proveit.logic import And, 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_both, conditions = [InSet(subtract(Add(j, one), i), Natural), Equals(Add(i, a), Add(k, b)), Equals(Add(j, a), Add(l, b))]), And(InSet(a, Integer), InSet(b, 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}, \left(i + a\right) = \left(k + b\right), \left(j + a\right) = \left(l + b\right)}~\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)\right) \textrm{ if } a \in \mathbb{Z} ,  b \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: 17 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Lambda	parameters: 9 body: 10
7	Operation	operator: 26 operands: 11
8	Operation	operator: 26 operands: 12
9	ExprTuple	64, 62, 52, 53
10	Conditional	value: 13 condition: 14
11	ExprTuple	65, 15
12	ExprTuple	67, 15
13	Operation	operator: 29 operands: 16
14	Operation	operator: 17 operands: 18
15	Literal
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	21, 22, 23
19	ExprTuple	24
20	ExprTuple	25
21	Operation	operator: 26 operands: 27
22	Operation	operator: 29 operands: 28
23	Operation	operator: 29 operands: 30
24	ExprRange	lambda_map: 31 start_index: 64 end_index: 62
25	ExprRange	lambda_map: 32 start_index: 52 end_index: 53
26	Literal
27	ExprTuple	33, 34
28	ExprTuple	35, 36
29	Literal
30	ExprTuple	37, 38
31	Lambda	parameter: 66 body: 39
32	Lambda	parameter: 66 body: 41
33	Operation	operator: 60 operands: 42
34	Literal
35	Operation	operator: 60 operands: 43
36	Operation	operator: 60 operands: 44
37	Operation	operator: 60 operands: 45
38	Operation	operator: 60 operands: 46
39	Operation	operator: 48 operand: 54
40	ExprTuple	66
41	Operation	operator: 48 operand: 55
42	ExprTuple	50, 51
43	ExprTuple	64, 65
44	ExprTuple	52, 67
45	ExprTuple	62, 65
46	ExprTuple	53, 67
47	ExprTuple	54
48	Variable
49	ExprTuple	55
50	Operation	operator: 60 operands: 56
51	Operation	operator: 57 operand: 64
52	Variable
53	Variable
54	Operation	operator: 60 operands: 59
55	Operation	operator: 60 operands: 61
56	ExprTuple	62, 63
57	Literal
58	ExprTuple	64
59	ExprTuple	66, 65
60	Literal
61	ExprTuple	66, 67
62	Variable
63	Literal
64	Variable
65	Variable
66	Variable
67	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 ¶