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Expression of type Equals

from the theory of proveit.logic.sets.unification

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 A_1_to_m
from proveit.logic import Equals, NotInSet, Union
from proveit.logic.sets import x_notin_all_A
In [2]:
# build up the expression from sub-expressions
expr = Equals(NotInSet(x, Union(A_1_to_m)), x_notin_all_A)
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(A_{1} \cup  A_{2} \cup  \ldots \cup  A_{m}\right)\right) = \left(\left(x \notin A_{1}\right) \land  \left(x \notin A_{2}\right) \land  \ldots \land  \left(x \notin A_{m}\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: 18
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple20, 8
6Literal
7ExprTuple9
8Operationoperator: 10
operands: 11
9ExprRangelambda_map: 12
start_index: 16
end_index: 17
10Literal
11ExprTuple13
12Lambdaparameter: 24
body: 14
13ExprRangelambda_map: 15
start_index: 16
end_index: 17
14Operationoperator: 18
operands: 19
15Lambdaparameter: 24
body: 21
16Literal
17Variable
18Literal
19ExprTuple20, 21
20Variable
21IndexedVarvariable: 22
index: 24
22Variable
23ExprTuple24
24Variable