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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 Conditional, Lambda, S, x, y
from proveit.logic import And, Difference, InSet, NotEquals, Set
In [2]:
# build up the expression from sub-expressions
expr = Lambda(x, Conditional(And(InSet(x, S), NotEquals(x, y)), InSet(x, Difference(S, Set(y)))))
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())
x \mapsto \left\{\left(x \in S\right) \land \left(x \neq y\right) \textrm{ if } x \in \left(S - \left\{y\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
0Lambdaparameter: 17
body: 2
1ExprTuple17
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operands: 6
4Operationoperator: 11
operands: 7
5Literal
6ExprTuple8, 9
7ExprTuple17, 10
8Operationoperator: 11
operands: 12
9Operationoperator: 13
operands: 14
10Operationoperator: 15
operands: 16
11Literal
12ExprTuple17, 18
13Literal
14ExprTuple17, 22
15Literal
16ExprTuple18, 19
17Variable
18Variable
19Operationoperator: 20
operand: 22
20Literal
21ExprTuple22
22Variable