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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 A, B, Conditional, Lambda, x
from proveit.logic import Equals, Forall, InSet, SetEquiv
In [2]:
# build up the expression from sub-expressions
expr = Lambda([A, B], Conditional(SetEquiv(A, B), Forall(instance_param_or_params = [x], instance_expr = Equals(InSet(x, A), InSet(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(A, B\right) \mapsto \left\{A \cong B \textrm{ if } \forall_{x}~\left(\left(x \in A\right) = \left(x \in B\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: 5
body: 1
1Conditionalvalue: 2
condition: 3
2Operationoperator: 4
operands: 5
3Operationoperator: 6
operand: 8
4Literal
5ExprTuple18, 20
6Literal
7ExprTuple8
8Lambdaparameter: 19
body: 10
9ExprTuple19
10Operationoperator: 11
operands: 12
11Literal
12ExprTuple13, 14
13Operationoperator: 16
operands: 15
14Operationoperator: 16
operands: 17
15ExprTuple19, 18
16Literal
17ExprTuple19, 20
18Variable
19Variable
20Variable