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Expression of type Conditional

from the theory of proveit.logic.sets.intersection

In [1]:
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, m, x
from proveit.core_expr_types import A_1_to_m
from proveit.logic import Forall, InSet, Intersect, NotInSet
from proveit.logic.sets import x_notin_some_A
from proveit.numbers import NaturalPos
In [2]:
# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [x, A_1_to_m], instance_expr = NotInSet(x, Intersect(A_1_to_m)), condition = x_notin_some_A), InSet(m, NaturalPos))
expr:
In [3]:
# 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
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\left\{\forall_{x, A_{1}, A_{2}, \ldots, A_{m}~|~\left(x \notin A_{1}\right) \lor  \left(x \notin A_{2}\right) \lor  \ldots \lor  \left(x \notin A_{m}\right)}~\left(x \notin \left(A_{1} \cap  A_{2} \cap  \ldots \cap  A_{m}\right)\right) \textrm{ if } m \in \mathbb{N}^+\right..
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 3
operand: 7
2Operationoperator: 5
operands: 6
3Literal
4ExprTuple7
5Literal
6ExprTuple25, 8
7Lambdaparameters: 9
body: 10
8Literal
9ExprTuple28, 21
10Conditionalvalue: 11
condition: 12
11Operationoperator: 26
operands: 13
12Operationoperator: 14
operands: 15
13ExprTuple28, 16
14Literal
15ExprTuple17
16Operationoperator: 18
operands: 19
17ExprRangelambda_map: 20
start_index: 24
end_index: 25
18Literal
19ExprTuple21
20Lambdaparameter: 32
body: 22
21ExprRangelambda_map: 23
start_index: 24
end_index: 25
22Operationoperator: 26
operands: 27
23Lambdaparameter: 32
body: 29
24Literal
25Variable
26Literal
27ExprTuple28, 29
28Variable
29IndexedVarvariable: 30
index: 32
30Variable
31ExprTuple32
32Variable