Metamath Proof Explorer


Theorem lsw0g

Description: The last symbol of an empty word does not exist. (Contributed by Alexander van der Vekens, 11-Nov-2018)

Ref Expression
Assertion lsw0g ⊢ lastS ⁡ ∅ = ∅

Proof

Step Hyp Ref Expression
1 wrd0 ⊢ ∅ ∈ Word V
2 hash0 ⊢ ∅ = 0
3 lsw0 ⊢ ∅ ∈ Word V ∧ ∅ = 0 → lastS ⁡ ∅ = ∅
4 1 2 3 mp2an ⊢ lastS ⁡ ∅ = ∅