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Expression of type Conditional

from the theory of proveit.logic.sets

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 Boolean, Forall, InSet, Intersect, SubsetEq
In [2]:
# build up the expression from sub-expressions
expr = Conditional(SubsetEq(Intersect(A, B), A), Forall(instance_param_or_params = [x], instance_expr = InSet(InSet(x, B), Boolean)))
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\{\left(A \cap B\right) \subseteq A \textrm{ if } \forall_{x}~\left(\left(x \in B\right) \in \mathbb{B}\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
operands: 4
2Operationoperator: 5
operand: 8
3Literal
4ExprTuple7, 13
5Literal
6ExprTuple8
7Operationoperator: 9
operands: 10
8Lambdaparameter: 19
body: 12
9Literal
10ExprTuple13, 20
11ExprTuple19
12Operationoperator: 17
operands: 14
13Variable
14ExprTuple15, 16
15Operationoperator: 17
operands: 18
16Literal
17Literal
18ExprTuple19, 20
19Variable
20Variable