logo

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 Lambda, S, x, y
from proveit.logic import And, Difference, Forall, InSet, NotEquals, Set
In [2]:
# build up the expression from sub-expressions
expr = Lambda([S, y], Forall(instance_param_or_params = [x], instance_expr = And(InSet(x, S), NotEquals(x, y)), domain = 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())
\left(S, y\right) \mapsto \left[\forall_{x \in S - \left\{y\right\}}~\left(\left(x \in S\right) \land \left(x \neq 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
0Lambdaparameters: 1
body: 2
1ExprTuple23, 27
2Operationoperator: 3
operand: 5
3Literal
4ExprTuple5
5Lambdaparameter: 22
body: 7
6ExprTuple22
7Conditionalvalue: 8
condition: 9
8Operationoperator: 10
operands: 11
9Operationoperator: 16
operands: 12
10Literal
11ExprTuple13, 14
12ExprTuple22, 15
13Operationoperator: 16
operands: 17
14Operationoperator: 18
operands: 19
15Operationoperator: 20
operands: 21
16Literal
17ExprTuple22, 23
18Literal
19ExprTuple22, 27
20Literal
21ExprTuple23, 24
22Variable
23Variable
24Operationoperator: 25
operand: 27
25Literal
26ExprTuple27
27Variable