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Expression of type Lambda

from the theory of proveit.logic.sets.equivalence

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, a, b, c, x
from proveit.logic import Equals, InSet, Set
from proveit.numbers import one, three, two
In [2]:
# build up the expression from sub-expressions
expr = Lambda(x, Equals(InSet(x, Set(one, two, three)), InSet(x, Set(a, b, c))))
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 \left\{1, 2, 3\right\}\right) = \left(x \in \left\{a, b, c\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: 11
body: 2
1ExprTuple11
2Operationoperator: 3
operands: 4
3Literal
4ExprTuple5, 6
5Operationoperator: 8
operands: 7
6Operationoperator: 8
operands: 9
7ExprTuple11, 10
8Literal
9ExprTuple11, 12
10Operationoperator: 14
operands: 13
11Variable
12Operationoperator: 14
operands: 15
13ExprTuple16, 17, 18
14Literal
15ExprTuple19, 20, 21
16Literal
17Literal
18Literal
19Variable
20Variable
21Variable