Existential instantiation
The principle of existential instantiation states that anything that is known to exist can be given a name, as long as that name is not already in use. Definitions make use of this principle by denoting numbers or other mathematical objects with unique letters.
Every object should be given a unique name upon creation. For example, in a proof that considers two even integers \(n\) and \(m\) that are not necessarily equal, they should be separately defined as \(n=2k\) and \(m=2j\) to avoid confusion between them.
⚠ Because of their similar-sounding names, existential instantiation may be incorrectly thought of as
the opposite of universal generalization. Be careful!
Logic & Proofs
Integer •
Rational number •
Inequality •
Real number •
Theorem •
Proof •
Statement •
Proof by exhaustion •
Universal generalization •
Counterexample •
Existence proof •
Existential instantiation •
Axiom •
Logic •
Truth •
Proposition •
Compound proposition •
Logical operation •
Logical equivalence •
Tautology •
Contradiction •
Logic law •
Predicate •
Domain •
Quantifier •
Argument •
Rule of inference •
Logical proof •
Direct proof •
Proof by contrapositive •
Irrational number •
Proof by contradiction •
Proof by cases •
Summation •
Disjunctive normal form
Set Theory
Set •
Element •
Empty set •
Universal set •
Subset •
Power set •
Cartesian product •
String •
Binary string •
Empty string •
Set operation •
Set identity •
Set proof
Functions
Algorithms
Relations
Number Theory
Induction
Combinatorics
Graph Theory
Graph •
Walk •
Subgraph •
Regular graph •
Complete graph •
Empty graph •
Cycle graph •
Hypercube graph •
Bipartite graph •
Component •
Eulerian circuit •
Eulerian trail •
Hamiltonian cycle •
Hamiltonian path •
Tree •
Huffman tree •
Substring •
Forest •
Path graph •
Star •
Spanning tree •
Weighted graph •
Minimum spanning tree •
Greedy algorithm •
Prim's algorithm
Recursion