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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 Conditional, Lambda, P, Px, x
from proveit.core_expr_types import Pk_a1_to_an, a_1_to_n
from proveit.logic import And, Forall, Set
In [2]:
# build up the expression from sub-expressions
expr = Lambda(P, Conditional(Forall(instance_param_or_params = [x], instance_expr = Px, domain = Set(a_1_to_n)), And(Pk_a1_to_an)))
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())
P \mapsto \left\{\forall_{x \in \left\{a_{1}, a_{2}, \ldots, a_{n}\right\}}~P\left(x\right) \textrm{ if } P\left(a_{1}\right) \land  P\left(a_{2}\right) \land  \ldots \land  P\left(a_{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
0Lambdaparameter: 19
body: 2
1ExprTuple19
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operand: 9
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple9
7Literal
8ExprTuple10
9Lambdaparameter: 21
body: 11
10ExprRangelambda_map: 12
start_index: 27
end_index: 28
11Conditionalvalue: 13
condition: 14
12Lambdaparameter: 32
body: 15
13Operationoperator: 19
operand: 21
14Operationoperator: 17
operands: 18
15Operationoperator: 19
operand: 29
16ExprTuple21
17Literal
18ExprTuple21, 22
19Variable
20ExprTuple29
21Variable
22Operationoperator: 23
operands: 24
23Literal
24ExprTuple25
25ExprRangelambda_map: 26
start_index: 27
end_index: 28
26Lambdaparameter: 32
body: 29
27Literal
28Variable
29IndexedVarvariable: 30
index: 32
30Variable
31ExprTuple32
32Variable