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Expression of type Equals

from the theory of proveit.logic.sets.enumeration

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 x
from proveit.core_expr_types import y_1_to_n
from proveit.logic import Equals, NotInSet, Set
from proveit.logic.sets import x_notequals_all_y
In [2]:
# build up the expression from sub-expressions
expr = Equals(NotInSet(x, Set(y_1_to_n)), x_notequals_all_y)
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(x \notin \left\{y_{1}, y_{2}, \ldots, y_{n}\right\}\right) = \left(\left(x \neq y_{1}\right) \land  \left(x \neq y_{2}\right) \land  \ldots \land  \left(x \neq y_{n}\right)\right)
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()()('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Operationoperator: 5
operands: 6
4Operationoperator: 7
operands: 8
5Literal
6ExprTuple21, 9
7Literal
8ExprTuple10
9Operationoperator: 11
operands: 12
10ExprRangelambda_map: 13
start_index: 17
end_index: 18
11Literal
12ExprTuple14
13Lambdaparameter: 25
body: 15
14ExprRangelambda_map: 16
start_index: 17
end_index: 18
15Operationoperator: 19
operands: 20
16Lambdaparameter: 25
body: 22
17Literal
18Variable
19Literal
20ExprTuple21, 22
21Variable
22IndexedVarvariable: 23
index: 25
23Variable
24ExprTuple25
25Variable