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Expression of type Conditional

from the theory of proveit.logic.sets.inclusion

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, B, Conditional, x
from proveit.logic import Forall, InSet, SubsetEq
In [2]:
# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [x], instance_expr = InSet(x, B), domain = A), SubsetEq(A, B))
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 A}~\left(x \in B\right) \textrm{ if } A \subseteq B\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
6ExprTuple17, 15
7Lambdaparameter: 16
body: 9
8ExprTuple16
9Conditionalvalue: 10
condition: 11
10Operationoperator: 13
operands: 12
11Operationoperator: 13
operands: 14
12ExprTuple16, 15
13Literal
14ExprTuple16, 17
15Variable
16Variable
17Variable