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.
# import Expression classes needed to build the expression
from proveit import ExprTuple, Lambda, P, Px, x
from proveit.core_expr_types import Pk_a1_to_an, a_1_to_n
from proveit.logic import And, Equals, Forall, Set

In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda(P, Equals(And(Pk_a1_to_an), Forall(instance_param_or_params = [x], instance_expr = Px, domain = Set(a_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(P \mapsto \left(\left(P\left(a_{1}\right) \land  P\left(a_{2}\right) \land  \ldots \land  P\left(a_{n}\right)\right) = \left[\forall_{x \in \left\{a_{1}, a_{2}, \ldots, a_{n}\right\}}~P\left(x\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
0ExprTuple1
1Lambdaparameter: 20
body: 3
2ExprTuple20
3Operationoperator: 4
operands: 5
4Literal
5ExprTuple6, 7
6Operationoperator: 8
operands: 9
7Operationoperator: 10
operand: 13
8Literal
9ExprTuple12
10Literal
11ExprTuple13
12ExprRangelambda_map: 14
start_index: 30
end_index: 31
13Lambdaparameter: 24
body: 15
14Lambdaparameter: 35
body: 16
15Conditionalvalue: 17
condition: 18
16Operationoperator: 20
operand: 32
17Operationoperator: 20
operand: 24
18Operationoperator: 22
operands: 23
19ExprTuple32
20Variable
21ExprTuple24
22Literal
23ExprTuple24, 25
24Variable
25Operationoperator: 26
operands: 27
26Literal
27ExprTuple28
28ExprRangelambda_map: 29
start_index: 30
end_index: 31
29Lambdaparameter: 35
body: 32
30Literal
31Variable
32IndexedVarvariable: 33
index: 35
33Variable
34ExprTuple35
35Variable