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Expression of type Conditional

from the theory of proveit.logic.equality

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
from proveit.core_expr_types import P__x_1_to_n, P__y_1_to_n, x_1_to_n, y_1_to_n
from proveit.logic import And, Equals
In [2]:
# build up the expression from sub-expressions
expr = Conditional(P__x_1_to_n, And(P__y_1_to_n, Equals([x_1_to_n], [y_1_to_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\{P\left(x_{1}, x_{2}, \ldots, x_{n}\right) \textrm{ if } P\left(y_{1}, y_{2}, \ldots, y_{n}\right) ,  \left(x_{1}, x_{2}, \ldots, x_{n}\right) = \left(y_{1}, y_{2}, \ldots, y_{n}\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: 7
operands: 10
2Operationoperator: 3
operands: 4
3Literal
4ExprTuple5, 6
5Operationoperator: 7
operands: 11
6Operationoperator: 8
operands: 9
7Variable
8Literal
9ExprTuple10, 11
10ExprTuple12
11ExprTuple13
12ExprRangelambda_map: 14
start_index: 16
end_index: 17
13ExprRangelambda_map: 15
start_index: 16
end_index: 17
14Lambdaparameter: 23
body: 18
15Lambdaparameter: 23
body: 19
16Literal
17Variable
18IndexedVarvariable: 20
index: 23
19IndexedVarvariable: 21
index: 23
20Variable
21Variable
22ExprTuple23
23Variable