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Expression of type Lambda

from the theory of proveit.numbers.multiplication

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, n
from proveit.core_expr_types import a_1_to_n
from proveit.logic import Forall, InSet
from proveit.numbers import Mult, Natural
In [2]:
# build up the expression from sub-expressions
expr = Lambda(n, Conditional(Forall(instance_param_or_params = [a_1_to_n], instance_expr = InSet(Mult(a_1_to_n), Natural), domain = Natural), InSet(n, Natural)))
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())
n \mapsto \left\{\forall_{a_{1}, a_{2}, \ldots, a_{n} \in \mathbb{N}}~\left(\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{n}\right) \in \mathbb{N}\right) \textrm{ if } n \in \mathbb{N}\right..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameter: 24
body: 2
1ExprTuple24
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operand: 8
4Operationoperator: 25
operands: 7
5Literal
6ExprTuple8
7ExprTuple24, 28
8Lambdaparameters: 18
body: 9
9Conditionalvalue: 10
condition: 11
10Operationoperator: 25
operands: 12
11Operationoperator: 13
operands: 14
12ExprTuple15, 28
13Literal
14ExprTuple16
15Operationoperator: 17
operands: 18
16ExprRangelambda_map: 19
start_index: 23
end_index: 24
17Literal
18ExprTuple20
19Lambdaparameter: 31
body: 21
20ExprRangelambda_map: 22
start_index: 23
end_index: 24
21Operationoperator: 25
operands: 26
22Lambdaparameter: 31
body: 27
23Literal
24Variable
25Literal
26ExprTuple27, 28
27IndexedVarvariable: 29
index: 31
28Literal
29Variable
30ExprTuple31
31Variable