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Expression of type Lambda

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, Lambda
from proveit.logic import And, Equals, ProperSubset, SetNotEquiv, SubsetEq
In [2]:
# build up the expression from sub-expressions
expr = Lambda([A, B], Equals(ProperSubset(A, B), And(SubsetEq(A, B), SetNotEquiv(B, A))))
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(A, B\right) \mapsto \left(\left(A \subset B\right) = \left(\left(A \subseteq B\right) \land \left(B \ncong A\right)\right)\right)
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameters: 12
body: 1
1Operationoperator: 2
operands: 3
2Literal
3ExprTuple4, 5
4Operationoperator: 6
operands: 12
5Operationoperator: 7
operands: 8
6Literal
7Literal
8ExprTuple9, 10
9Operationoperator: 11
operands: 12
10Operationoperator: 13
operands: 14
11Literal
12ExprTuple16, 15
13Literal
14ExprTuple15, 16
15Variable
16Variable