Expression of type Conditional ¶

from the theory of proveit.numbers.numerals.decimals ¶

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, ExprRange, IndexedVar, Variable, a, b, k, m
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Add, DecimalSequence, Digits, Less, Natural, nine, one, zero

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = ExprRange(sub_expr1, IndexedVar(a, sub_expr1), one, m)
expr = Conditional(Forall(instance_param_or_params = [sub_expr2, b], instance_expr = Equals(Add(DecimalSequence(sub_expr2, b, ExprRange(sub_expr1, nine, one, k)), one), DecimalSequence(sub_expr2, Add(b, one), ExprRange(sub_expr1, zero, one, k))), domain = Digits, condition = Less(b, nine)), And(InSet(m, Natural), InSet(k, Natural)))

# 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_{a_{1}, a_{2}, \ldots, a_{m}, b \in \mathbb{N}^{\leq 9}~|~b < 9}~\left(\left(\texttt{\#}(a_{1}, a_{2}, \ldots, a_{m} ~ b ~ 9, 9, ..\left(k - 3\right) \times.., 9) + 1\right) = \texttt{\#}(a_{1}, a_{2}, \ldots, a_{m} ~ \left(b + 1\right) ~ 0, 0, ..\left(k - 3\right) \times.., 0)\right) \textrm{ if } m \in \mathbb{N} ,  k \in \mathbb{N}\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: 18 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Lambda	parameters: 9 body: 10
7	Operation	operator: 40 operands: 11
8	Operation	operator: 40 operands: 12
9	ExprTuple	42, 44
10	Conditional	value: 13 condition: 14
11	ExprTuple	48, 15
12	ExprTuple	51, 15
13	Operation	operator: 16 operands: 17
14	Operation	operator: 18 operands: 19
15	Literal
16	Literal
17	ExprTuple	20, 21
18	Literal
19	ExprTuple	22, 23, 24
20	Operation	operator: 37 operands: 25
21	Operation	operator: 35 operands: 26
22	ExprRange	lambda_map: 27 start_index: 50 end_index: 48
23	Operation	operator: 40 operands: 28
24	Operation	operator: 29 operands: 30
25	ExprTuple	31, 50
26	ExprTuple	42, 32, 33
27	Lambda	parameter: 56 body: 34
28	ExprTuple	44, 46
29	Literal
30	ExprTuple	44, 53
31	Operation	operator: 35 operands: 36
32	Operation	operator: 37 operands: 38
33	ExprRange	lambda_map: 39 start_index: 50 end_index: 51
34	Operation	operator: 40 operands: 41
35	Literal
36	ExprTuple	42, 44, 43
37	Literal
38	ExprTuple	44, 50
39	Lambda	parameter: 56 body: 45
40	Literal
41	ExprTuple	52, 46
42	ExprRange	lambda_map: 47 start_index: 50 end_index: 48
43	ExprRange	lambda_map: 49 start_index: 50 end_index: 51
44	Variable
45	Literal
46	Literal
47	Lambda	parameter: 56 body: 52
48	Variable
49	Lambda	parameter: 56 body: 53
50	Literal
51	Variable
52	IndexedVar	variable: 54 index: 56
53	Literal
54	Variable
55	ExprTuple	56
56	Variable

Expression of type Conditional¶

from the theory of proveit.numbers.numerals.decimals¶

Expression of type Conditional ¶

from the theory of proveit.numbers.numerals.decimals ¶