logo

Expression of type Conditional

from the theory of proveit.logic.booleans

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 A, Conditional, PofA
from proveit.logic import And, Boolean, Forall, PofFalse, PofTrue
In [2]:
# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [A], instance_expr = PofA, domain = Boolean), And(PofTrue, PofFalse))
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_{A \in \mathbb{B}}~P\left(A\right) \textrm{ if } P\left(\top\right) ,  P\left(\bot\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, 9
7Lambdaparameter: 21
body: 10
8Operationoperator: 17
operand: 15
9Operationoperator: 17
operand: 16
10Conditionalvalue: 13
condition: 14
11ExprTuple15
12ExprTuple16
13Operationoperator: 17
operand: 21
14Operationoperator: 19
operands: 20
15Literal
16Literal
17Variable
18ExprTuple21
19Literal
20ExprTuple21, 22
21Variable
22Literal