Step
*
2
1
of Lemma
before_last
1. [T] : Type
2. u : T
3. v : T List
4. ∀x:T. ((x ∈ v)
⇒ x before last(v) ∈ v supposing ¬(x = last(v) ∈ T))
5. x : T
6. (x = u ∈ T) ∨ (x ∈ v)
7. ¬(x = last([u / v]) ∈ T)
⊢ x before last([u / v]) ∈ [u / v]
BY
{ ((((Unfold `l_before` 0 THEN RWO "cons_sublist_cons" 0) THEN Auto) THEN Reduce 0) THEN SimpConcl) }
1
1. [T] : Type
2. u : T
3. v : T List
4. ∀x:T. ((x ∈ v)
⇒ x before last(v) ∈ v supposing ¬(x = last(v) ∈ T))
5. x : T
6. (x = u ∈ T) ∨ (x ∈ v)
7. ¬(x = last([u / v]) ∈ T)
⊢ ((x = u ∈ T) ∧ [last([u / v])] ⊆ v) ∨ [x; last([u / v])] ⊆ v
Latex:
Latex:
1. [T] : Type
2. u : T
3. v : T List
4. \mforall{}x:T. ((x \mmember{} v) {}\mRightarrow{} x before last(v) \mmember{} v supposing \mneg{}(x = last(v)))
5. x : T
6. (x = u) \mvee{} (x \mmember{} v)
7. \mneg{}(x = last([u / v]))
\mvdash{} x before last([u / v]) \mmember{} [u / v]
By
Latex:
((((Unfold `l\_before` 0 THEN RWO "cons\_sublist\_cons" 0) THEN Auto) THEN Reduce 0) THEN SimpConcl)
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