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Expression of type Conditional

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, 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 = 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())
\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()
namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 3
operand: 6
2Operationoperator: 23
operands: 5
3Literal
4ExprTuple6
5ExprTuple22, 26
6Lambdaparameters: 16
body: 7
7Conditionalvalue: 8
condition: 9
8Operationoperator: 23
operands: 10
9Operationoperator: 11
operands: 12
10ExprTuple13, 26
11Literal
12ExprTuple14
13Operationoperator: 15
operands: 16
14ExprRangelambda_map: 17
start_index: 21
end_index: 22
15Literal
16ExprTuple18
17Lambdaparameter: 29
body: 19
18ExprRangelambda_map: 20
start_index: 21
end_index: 22
19Operationoperator: 23
operands: 24
20Lambdaparameter: 29
body: 25
21Literal
22Variable
23Literal
24ExprTuple25, 26
25IndexedVarvariable: 27
index: 29
26Literal
27Variable
28ExprTuple29
29Variable