logo

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, NotEquals
from proveit.numbers import ComplexNonZero, Mult, Natural, zero
In [2]:
# build up the expression from sub-expressions
expr = Lambda(n, Conditional(Forall(instance_param_or_params = [a_1_to_n], instance_expr = NotEquals(Mult(a_1_to_n), zero), domain = ComplexNonZero), 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{C}^{\neq 0}}~\left(\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{n}\right) \neq 0\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: 27
body: 2
1ExprTuple27
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operand: 8
4Operationoperator: 28
operands: 7
5Literal
6ExprTuple8
7ExprTuple27, 9
8Lambdaparameters: 21
body: 10
9Literal
10Conditionalvalue: 11
condition: 12
11Operationoperator: 13
operands: 14
12Operationoperator: 15
operands: 16
13Literal
14ExprTuple17, 18
15Literal
16ExprTuple19
17Operationoperator: 20
operands: 21
18Literal
19ExprRangelambda_map: 22
start_index: 26
end_index: 27
20Literal
21ExprTuple23
22Lambdaparameter: 34
body: 24
23ExprRangelambda_map: 25
start_index: 26
end_index: 27
24Operationoperator: 28
operands: 29
25Lambdaparameter: 34
body: 30
26Literal
27Variable
28Literal
29ExprTuple30, 31
30IndexedVarvariable: 32
index: 34
31Literal
32Variable
33ExprTuple34
34Variable