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Expression of type Lambda

from the theory of proveit.logic.sets.intersection

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 Conditional, Lambda, x
from proveit.core_expr_types import A_1_to_m
from proveit.logic import InSet, Intersect
from proveit.logic.sets import x_in_every_A
In [2]:
# build up the expression from sub-expressions
expr = Lambda([x, A_1_to_m], Conditional(x_in_every_A, InSet(x, Intersect(A_1_to_m))))
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(x, A_{1}, A_{2}, \ldots, A_{m}\right) \mapsto \left\{\left(x \in A_{1}\right) \land  \left(x \in A_{2}\right) \land  \ldots \land  \left(x \in A_{m}\right) \textrm{ if } x \in \left(A_{1} \cap  A_{2} \cap  \ldots \cap  A_{m}\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
1ExprTuple20, 14
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operands: 6
4Operationoperator: 15
operands: 7
5Literal
6ExprTuple8
7ExprTuple20, 9
8ExprRangelambda_map: 10
start_index: 18
end_index: 19
9Operationoperator: 11
operands: 12
10Lambdaparameter: 24
body: 13
11Literal
12ExprTuple14
13Operationoperator: 15
operands: 16
14ExprRangelambda_map: 17
start_index: 18
end_index: 19
15Literal
16ExprTuple20, 21
17Lambdaparameter: 24
body: 21
18Literal
19Variable
20Variable
21IndexedVarvariable: 22
index: 24
22Variable
23ExprTuple24
24Variable