logo

Expression of type And

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 ExprRange, IndexedVar, Variable, n, x
from proveit.logic import And, Equals
from proveit.numbers import Add, one
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = And(ExprRange(sub_expr1, Equals(IndexedVar(x, sub_expr1), IndexedVar(x, Add(sub_expr1, one))), one, n))
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_{1} = x_{1 + 1}\right) \land  \left(x_{2} = x_{2 + 1}\right) \land  \ldots \land  \left(x_{n} = x_{n + 1}\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',)
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3
3ExprRangelambda_map: 4
start_index: 18
end_index: 5
4Lambdaparameter: 17
body: 6
5Variable
6Operationoperator: 7
operands: 8
7Literal
8ExprTuple9, 10
9IndexedVarvariable: 12
index: 17
10IndexedVarvariable: 12
index: 14
11ExprTuple17
12Variable
13ExprTuple14
14Operationoperator: 15
operands: 16
15Literal
16ExprTuple17, 18
17Variable
18Literal