---

Step * of Lemma cont-induction

∀[P:ℕ ⟶ ℙ]. (P[0] ⇒ (∀n:ℕ. (P[n] ⇒ P[n + 1])) ⇒ (∀n:ℕ. P[n]))
BY
{ (Auto THEN (InstLemma `cont-induction-lemma` [⌜P⌝;⌜n⌝;⌜0⌝]⋅ THENA Auto)) }

1
1. [P] : ℕ ⟶ ℙ
2. P[0]@i
3. ∀n:ℕ. (P[n] ⇒ P[n + 1])@i
4. n : ℕ@i
5. P[n + 0]
⊢ P[n]

---

Latex:

---

Latex:
\mforall{}[P:\mBbbN{}  {}\mrightarrow{}  \mBbbP{}].  (P[0]  {}\mRightarrow{}  (\mforall{}n:\mBbbN{}.  (P[n]  {}\mRightarrow{}  P[n  +  1]))  {}\mRightarrow{}  (\mforall{}n:\mBbbN{}.  P[n]))


By

---

Latex:
(Auto  THEN  (InstLemma  `cont-induction-lemma`  [\mkleeneopen{}P\mkleeneclose{};\mkleeneopen{}n\mkleeneclose{};\mkleeneopen{}0\mkleeneclose{}]\mcdot{}  THENA  Auto))

---

Home Index