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Expression of type Equals

from the theory of proveit.numbers.addition

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 ExprRange, IndexedVar, Variable, a, b, c, m
from proveit.core_expr_types import a_1_to_n
from proveit.logic import Equals
from proveit.numbers import Add, Neg, one, subtract
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Neg(c)
sub_expr3 = ExprRange(sub_expr1, IndexedVar(a, sub_expr1), one, m)
sub_expr4 = Add(a_1_to_n)
expr = Equals(Add(Add(sub_expr3, b), subtract(sub_expr2, sub_expr4)), Add(sub_expr3, b, sub_expr2, Neg(sub_expr4)))
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(\left(a_{1} +  a_{2} +  \ldots +  a_{m} + b\right) + \left(-c - \left(a_{1} +  a_{2} +  \ldots +  a_{n}\right)\right)\right) = \left(a_{1} +  a_{2} +  \ldots +  a_{m} + b - c - \left(a_{1} +  a_{2} +  \ldots +  a_{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: 21
operands: 5
4Operationoperator: 21
operands: 6
5ExprTuple7, 8
6ExprTuple11, 12, 13, 14
7Operationoperator: 21
operands: 9
8Operationoperator: 21
operands: 10
9ExprTuple11, 12
10ExprTuple13, 14
11ExprRangelambda_map: 24
start_index: 25
end_index: 15
12Variable
13Operationoperator: 17
operand: 19
14Operationoperator: 17
operand: 20
15Variable
16ExprTuple19
17Literal
18ExprTuple20
19Variable
20Operationoperator: 21
operands: 22
21Literal
22ExprTuple23
23ExprRangelambda_map: 24
start_index: 25
end_index: 26
24Lambdaparameter: 30
body: 27
25Literal
26Variable
27IndexedVarvariable: 28
index: 30
28Variable
29ExprTuple30
30Variable