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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, f, n
from proveit.core_expr_types import f__x_1_to_n, f__y_1_to_n, x_1_to_n, x_eq_y__1_to_n, y_1_to_n
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import NaturalPos
In [2]:
# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [f, x_1_to_n, y_1_to_n], instance_expr = Equals(f__x_1_to_n, f__y_1_to_n), condition = x_eq_y__1_to_n), InSet(n, NaturalPos))
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_{f, x_{1}, x_{2}, \ldots, x_{n}, y_{1}, y_{2}, \ldots, y_{n}~|~\left(x_{1} = y_{1}\right), \left(x_{2} = y_{2}\right), \ldots, \left(x_{n} = y_{n}\right)}~\left(f\left(x_{1}, x_{2}, \ldots, x_{n}\right) = f\left(y_{1}, y_{2}, \ldots, y_{n}\right)\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: 7
2Operationoperator: 5
operands: 6
3Literal
4ExprTuple7
5Literal
6ExprTuple29, 8
7Lambdaparameters: 9
body: 10
8Literal
9ExprTuple20, 23, 24
10Conditionalvalue: 11
condition: 12
11Operationoperator: 30
operands: 13
12Operationoperator: 14
operands: 15
13ExprTuple16, 17
14Literal
15ExprTuple18
16Operationoperator: 20
operands: 19
17Operationoperator: 20
operands: 21
18ExprRangelambda_map: 22
start_index: 28
end_index: 29
19ExprTuple23
20Variable
21ExprTuple24
22Lambdaparameter: 37
body: 25
23ExprRangelambda_map: 26
start_index: 28
end_index: 29
24ExprRangelambda_map: 27
start_index: 28
end_index: 29
25Operationoperator: 30
operands: 31
26Lambdaparameter: 37
body: 32
27Lambdaparameter: 37
body: 33
28Literal
29Variable
30Literal
31ExprTuple32, 33
32IndexedVarvariable: 34
index: 37
33IndexedVarvariable: 35
index: 37
34Variable
35Variable
36ExprTuple37
37Variable