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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, ExprRange, IndexedVar, Variable, a, n
from proveit.core_expr_types import a_1_to_n
from proveit.logic import And, InSet, NotEquals
from proveit.numbers import ComplexNonZero, Mult, one, zero
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(NotEquals(Mult(a_1_to_n), zero), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), ComplexNonZero), one, 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\{\left(a_{1} \cdot  a_{2} \cdot  \ldots \cdot  a_{n}\right) \neq 0 \textrm{ if } \left(a_{1} \in \mathbb{C}^{\neq 0}\right) \land  \left(a_{2} \in \mathbb{C}^{\neq 0}\right) \land  \ldots \land  \left(a_{n} \in \mathbb{C}^{\neq 0}\right)\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
operands: 4
2Operationoperator: 5
operands: 6
3Literal
4ExprTuple7, 8
5Literal
6ExprTuple9
7Operationoperator: 10
operands: 11
8Literal
9ExprRangelambda_map: 12
start_index: 16
end_index: 17
10Literal
11ExprTuple13
12Lambdaparameter: 24
body: 14
13ExprRangelambda_map: 15
start_index: 16
end_index: 17
14Operationoperator: 18
operands: 19
15Lambdaparameter: 24
body: 20
16Literal
17Variable
18Literal
19ExprTuple20, 21
20IndexedVarvariable: 22
index: 24
21Literal
22Variable
23ExprTuple24
24Variable