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Expression of type Lambda

from the theory of proveit.logic.sets.subtraction

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, Lambda, x
from proveit.logic import And, Difference, InSet, NotInSet
In [2]:
# build up the expression from sub-expressions
expr = Lambda([x, A, B], Conditional(InSet(x, Difference(A, B)), And(InSet(x, A), NotInSet(x, 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(x, A, B\right) \mapsto \left\{x \in \left(A - B\right) \textrm{ if } x \in A ,  x \notin B\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameters: 1
body: 2
1ExprTuple18, 17, 19
2Conditionalvalue: 3
condition: 4
3Operationoperator: 13
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple18, 8
6Literal
7ExprTuple9, 10
8Operationoperator: 11
operands: 12
9Operationoperator: 13
operands: 14
10Operationoperator: 15
operands: 16
11Literal
12ExprTuple17, 19
13Literal
14ExprTuple18, 17
15Literal
16ExprTuple18, 19
17Variable
18Variable
19Variable