Step
*
of Lemma
cons_member
∀[T:Type]. ∀l:T List. ∀a,x:T. ((x ∈ [a / l])
⇐⇒ (x = a ∈ T) ∨ (x ∈ l))
BY
{ (Unfold `l_member` 0 THEN Auto) }
1
1. [T] : Type
2. l : T List
3. a : T
4. x : T
5. ∃i:ℕ. (i < ||[a / l]|| c∧ (x = [a / l][i] ∈ T))
⊢ (x = a ∈ T) ∨ (∃i:ℕ. (i < ||l|| c∧ (x = l[i] ∈ T)))
2
1. [T] : Type
2. l : T List
3. a : T
4. x : T
5. (x = a ∈ T) ∨ (∃i:ℕ. (i < ||l|| c∧ (x = l[i] ∈ T)))
⊢ ∃i:ℕ. (i < ||[a / l]|| c∧ (x = [a / l][i] ∈ T))
Latex:
Latex:
\mforall{}[T:Type]. \mforall{}l:T List. \mforall{}a,x:T. ((x \mmember{} [a / l]) \mLeftarrow{}{}\mRightarrow{} (x = a) \mvee{} (x \mmember{} l))
By
Latex:
(Unfold `l\_member` 0 THEN Auto)
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