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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 f__x_1_to_n, f__y_1_to_n, x_eq_y__1_to_n
from proveit.logic import And, Equals
In [2]:
# build up the expression from sub-expressions
expr = Conditional(Equals(f__x_1_to_n, f__y_1_to_n), And(x_eq_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\{f\left(x_{1}, x_{2}, \ldots, x_{n}\right) = f\left(y_{1}, y_{2}, \ldots, y_{n}\right) \textrm{ if } \left(x_{1} = y_{1}\right) \land  \left(x_{2} = y_{2}\right) \land  \ldots \land  \left(x_{n} = 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: 20
operands: 3
2Operationoperator: 4
operands: 5
3ExprTuple6, 7
4Literal
5ExprTuple8
6Operationoperator: 10
operands: 9
7Operationoperator: 10
operands: 11
8ExprRangelambda_map: 12
start_index: 18
end_index: 19
9ExprTuple13
10Variable
11ExprTuple14
12Lambdaparameter: 27
body: 15
13ExprRangelambda_map: 16
start_index: 18
end_index: 19
14ExprRangelambda_map: 17
start_index: 18
end_index: 19
15Operationoperator: 20
operands: 21
16Lambdaparameter: 27
body: 22
17Lambdaparameter: 27
body: 23
18Literal
19Variable
20Literal
21ExprTuple22, 23
22IndexedVarvariable: 24
index: 27
23IndexedVarvariable: 25
index: 27
24Variable
25Variable
26ExprTuple27
27Variable