Expression of type Conditional ¶

from the theory of proveit.numbers.modular ¶

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, L, S, c, x
from proveit.logic import Card, Equals, Forall, SetOfAll, SubsetEq
from proveit.numbers import Add, Mod, Real

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = Conditional(Forall(instance_param_or_params = [c], instance_expr = Equals(Card(SetOfAll(instance_param_or_params = sub_expr1, instance_element = Mod(Add(x, c), L), domain = S)), Card(SetOfAll(instance_param_or_params = sub_expr1, instance_element = Mod(x, L), domain = S))), domain = Real), SubsetEq(S, Real))

# 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_{c \in \mathbb{R}}~\left(|\left\{\left(x + c\right) ~\textup{mod}~ L\right\}_{x \in S}| = |\left\{x ~\textup{mod}~ L\right\}_{x \in S}|\right) \textrm{ if } S \subseteq \mathbb{R}\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: 7
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	41, 17
7	Lambda	parameter: 45 body: 9
8	ExprTuple	45
9	Conditional	value: 10 condition: 11
10	Operation	operator: 12 operands: 13
11	Operation	operator: 37 operands: 14
12	Literal
13	ExprTuple	15, 16
14	ExprTuple	45, 17
15	Operation	operator: 19 operand: 21
16	Operation	operator: 19 operand: 22
17	Literal
18	ExprTuple	21
19	Literal
20	ExprTuple	22
21	Operation	operator: 24 operand: 26
22	Operation	operator: 24 operand: 27
23	ExprTuple	26
24	Literal
25	ExprTuple	27
26	Lambda	parameter: 44 body: 28
27	Lambda	parameter: 44 body: 30
28	Conditional	value: 31 condition: 33
29	ExprTuple	44
30	Conditional	value: 32 condition: 33
31	Operation	operator: 35 operands: 34
32	Operation	operator: 35 operands: 36
33	Operation	operator: 37 operands: 38
34	ExprTuple	39, 40
35	Literal
36	ExprTuple	44, 40
37	Literal
38	ExprTuple	44, 41
39	Operation	operator: 42 operands: 43
40	Variable
41	Variable
42	Literal
43	ExprTuple	44, 45
44	Variable
45	Variable

Expression of type Conditional¶

from the theory of proveit.numbers.modular¶

Expression of type Conditional ¶

from the theory of proveit.numbers.modular ¶