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Expression of type Lambda

from the theory of proveit.logic.sets.enumeration

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
from proveit.core_expr_types import a_1_to_m, b_1_to_n
from proveit.logic import Set, SubsetEq
In [2]:
# build up the expression from sub-expressions
expr = Lambda([a_1_to_m, b_1_to_n], SubsetEq(Set(a_1_to_m), Set(a_1_to_m, b_1_to_n)))
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_{1}, a_{2}, \ldots, a_{m}, b_{1}, b_{2}, \ldots, b_{n}\right) \mapsto \left(\left\{a_{1}, a_{2}, \ldots, a_{m}\right\} \subseteq \left\{a_{1}, a_{2}, \ldots, a_{m},b_{1}, b_{2}, \ldots, b_{n}\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: 8
body: 1
1Operationoperator: 2
operands: 3
2Literal
3ExprTuple4, 5
4Operationoperator: 7
operands: 6
5Operationoperator: 7
operands: 8
6ExprTuple9
7Literal
8ExprTuple9, 10
9ExprRangelambda_map: 11
start_index: 14
end_index: 12
10ExprRangelambda_map: 13
start_index: 14
end_index: 15
11Lambdaparameter: 21
body: 16
12Variable
13Lambdaparameter: 21
body: 17
14Literal
15Variable
16IndexedVarvariable: 18
index: 21
17IndexedVarvariable: 19
index: 21
18Variable
19Variable
20ExprTuple21
21Variable