logo

Expression of type Forall

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 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
from proveit.numbers import NaturalPos
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [n], instance_expr = 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), domain = 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())
\forall_{n \in \mathbb{N}^+}~\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)\right]
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
condition_wrappingWrap 'before' or 'after' the condition (or None).NoneNone/False('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_paramsIf 'True', wraps every two parameters AND wraps the Expression after the parametersNoneNone/False('with_params',)
justificationjustify to the 'left', 'center', or 'right' in the array cellscentercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 7
operand: 2
1ExprTuple2
2Lambdaparameter: 33
body: 4
3ExprTuple33
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 11
6Operationoperator: 9
operands: 10
7Literal
8ExprTuple11
9Literal
10ExprTuple33, 12
11Lambdaparameters: 13
body: 14
12Literal
13ExprTuple24, 27, 28
14Conditionalvalue: 15
condition: 16
15Operationoperator: 34
operands: 17
16Operationoperator: 18
operands: 19
17ExprTuple20, 21
18Literal
19ExprTuple22
20Operationoperator: 24
operands: 23
21Operationoperator: 24
operands: 25
22ExprRangelambda_map: 26
start_index: 32
end_index: 33
23ExprTuple27
24Variable
25ExprTuple28
26Lambdaparameter: 41
body: 29
27ExprRangelambda_map: 30
start_index: 32
end_index: 33
28ExprRangelambda_map: 31
start_index: 32
end_index: 33
29Operationoperator: 34
operands: 35
30Lambdaparameter: 41
body: 36
31Lambdaparameter: 41
body: 37
32Literal
33Variable
34Literal
35ExprTuple36, 37
36IndexedVarvariable: 38
index: 41
37IndexedVarvariable: 39
index: 41
38Variable
39Variable
40ExprTuple41
41Variable