logo

Expression of type Conditional

from the theory of proveit.logic.sets.enumeration

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, Px, x
from proveit.core_expr_types import Pk_a1_to_an, a_1_to_n
from proveit.logic import And, Forall, Set
In [2]:
# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [x], instance_expr = Px, domain = Set(a_1_to_n)), And(Pk_a1_to_an))
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 \in \left\{a_{1}, a_{2}, \ldots, a_{n}\right\}}~P\left(x\right) \textrm{ if } P\left(a_{1}\right) \land  P\left(a_{2}\right) \land  \ldots \land  P\left(a_{n}\right)\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
6ExprTuple8
7Lambdaparameter: 19
body: 9
8ExprRangelambda_map: 10
start_index: 25
end_index: 26
9Conditionalvalue: 11
condition: 12
10Lambdaparameter: 30
body: 13
11Operationoperator: 17
operand: 19
12Operationoperator: 15
operands: 16
13Operationoperator: 17
operand: 27
14ExprTuple19
15Literal
16ExprTuple19, 20
17Variable
18ExprTuple27
19Variable
20Operationoperator: 21
operands: 22
21Literal
22ExprTuple23
23ExprRangelambda_map: 24
start_index: 25
end_index: 26
24Lambdaparameter: 30
body: 27
25Literal
26Variable
27IndexedVarvariable: 28
index: 30
28Variable
29ExprTuple30
30Variable