Lemmas for the linear_combination tactic #
These should not be used directly in user code.
Addition #
Multiplication #
Scalar multiplication #
Division #
Lemmas constructing the reduction of a goal to a specified built-up hypothesis #
Alias of the forward direction of sub_eq_zero
.
Lookup functions for lemmas by operation and relation(s) #
Given two (in)equalities, look up the lemma to add them.
Equations
Instances For
Finite inductive type extending Mathlib.Ineq
: a type of inequality (eq
, le
or lt
),
together with, in the case of lt
, a boolean, typically representing the strictness (< or ≤) of
some other inequality.
- eq : Ineq.WithStrictness
- le : Ineq.WithStrictness
- lt (strict : Bool) : Ineq.WithStrictness
Instances For
Given an (in)equality, look up the lemma to left-multiply it by a constant. If relevant, also take into account the degree of positivity which can be proved of the constant: strict or non-strict.
Equations
Instances For
Given an (in)equality, look up the lemma to right-multiply it by a constant. If relevant, also take into account the degree of positivity which can be proved of the constant: strict or non-strict.
Equations
Instances For
Given an (in)equality, look up the lemma to left-scalar-multiply it by a constant (scalar). If relevant, also take into account the degree of positivity which can be proved of the constant: strict or non-strict.
Equations
Instances For
Given an (in)equality, look up the lemma to right-scalar-multiply it by a constant (vector). If relevant, also take into account the degree of positivity which can be proved of the constant: strict or non-strict.
Equations
Instances For
Given an (in)equality, look up the lemma to divide it by a constant. If relevant, also take into account the degree of positivity which can be proved of the constant: strict or non-strict.
Equations
Instances For
Given an (in)equality, look up the lemma to move everything to the LHS.