Expression of type Conditional ¶

from the theory of proveit.logic.sets.cardinality ¶

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, N, S, n
from proveit.core_expr_types import Len, x_1_to_n
from proveit.logic import Card, Distinct, Equals, Exists, Forall, InSet
from proveit.numbers import NaturalPos, greater_eq

# build up the expression from sub-expressions
sub_expr1 = [x_1_to_n]
expr = Conditional(Forall(instance_param_or_params = [S, N], instance_expr = Exists(instance_param_or_params = sub_expr1, instance_expr = Distinct(x_1_to_n), domain = S, condition = Equals(Len(operands = sub_expr1), N)), condition = greater_eq(Card(S), N)), InSet(n, NaturalPos))

# 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_{S, N~|~|S| \geq N}~\left[\exists_{x_{1}, x_{2}, \ldots, x_{n} \in S~|~|\left(x_{1}, x_{2}, \ldots, x_{n}\right)| = N}~\textrm{distinct}\left(x_{1}, x_{2}, \ldots, x_{n}\right)\right] \textrm{ if } n \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: 34 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	42, 7
6	Lambda	parameters: 8 body: 9
7	Literal
8	ExprTuple	38, 33
9	Conditional	value: 10 condition: 11
10	Operation	operator: 12 operand: 16
11	Operation	operator: 14 operands: 15
12	Literal
13	ExprTuple	16
14	Literal
15	ExprTuple	33, 17
16	Lambda	parameters: 37 body: 18
17	Operation	operator: 19 operand: 38
18	Conditional	value: 21 condition: 22
19	Literal
20	ExprTuple	38
21	Operation	operator: 23 operands: 37
22	Operation	operator: 24 operands: 25
23	Literal
24	Literal
25	ExprTuple	26, 27
26	ExprRange	lambda_map: 28 start_index: 41 end_index: 42
27	Operation	operator: 29 operands: 30
28	Lambda	parameter: 46 body: 31
29	Literal
30	ExprTuple	32, 33
31	Operation	operator: 34 operands: 35
32	Operation	operator: 36 operands: 37
33	Variable
34	Literal
35	ExprTuple	43, 38
36	Literal
37	ExprTuple	39
38	Variable
39	ExprRange	lambda_map: 40 start_index: 41 end_index: 42
40	Lambda	parameter: 46 body: 43
41	Literal
42	Variable
43	IndexedVar	variable: 44 index: 46
44	Variable
45	ExprTuple	46
46	Variable

Expression of type Conditional¶

from the theory of proveit.logic.sets.cardinality¶

Expression of type Conditional ¶

from the theory of proveit.logic.sets.cardinality ¶