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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 Lambda, S, x, y
from proveit.logic import 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 = InSet(x, Difference(S, Set(y))), domain = S, condition = NotEquals(x, 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~|~x \neq y}~\left(x \in \left(S - \left\{y\right\}\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: 24
body: 7
6ExprTuple24
7Conditionalvalue: 8
condition: 9
8Operationoperator: 18
operands: 10
9Operationoperator: 11
operands: 12
10ExprTuple24, 13
11Literal
12ExprTuple14, 15
13Operationoperator: 16
operands: 17
14Operationoperator: 18
operands: 19
15Operationoperator: 20
operands: 21
16Literal
17ExprTuple23, 22
18Literal
19ExprTuple24, 23
20Literal
21ExprTuple24, 27
22Operationoperator: 25
operand: 27
23Variable
24Variable
25Literal
26ExprTuple27
27Variable