Theorem: all_from_three_five (BrownCs22/Homework/Hw9.lean)

State before:
P : ℕ → Prop
⊢ ∀ (n : ℕ), 8 ≤ n → from_three_five n
Tactic:
strong_induction
State after:
P : ℕ → Prop
⊢ ∀ (n : ℕ), (∀ (m : ℕ), m < n → 8 ≤ m → from_three_five m) → 8 ≤ n → from_three_five n

State before:
P : ℕ → Prop
⊢ ∀ (n : ℕ), (∀ (m : ℕ), m < n → 8 ≤ m → from_three_five m) → 8 ≤ n → from_three_five n
Tactic:
intro n hind h
State after:
P : ℕ → Prop
n : ℕ
hind : ∀ (m : ℕ), m < n → 8 ≤ m → from_three_five m
h : 8 ≤ n
⊢ from_three_five n

State before:
P : ℕ → Prop
n : ℕ
hind : ∀ (m : ℕ), m < n → 8 ≤ m → from_three_five m
h : 8 ≤ n
⊢ from_three_five n
Tactic:
eliminate (lt_or_le n 11) with htri htri
State after:
case inl
P : ℕ → Prop
n : ℕ
hind : ∀ (m : ℕ), m < n → 8 ≤ m → from_three_five m
h : 8 ≤ n
htri : n < 11
⊢ from_three_five n

case inr
P : ℕ → Prop
n : ℕ
hind : ∀ (m : ℕ), m < n → 8 ≤ m → from_three_five m
h : 8 ≤ n
htri : 11 ≤ n
⊢ from_three_five n

State before:
case inl
P : ℕ → Prop
n : ℕ
hind : ∀ (m : ℕ), m < n → 8 ≤ m → from_three_five m
h : 8 ≤ n
htri : n < 11
⊢ from_three_five n

case inr
P : ℕ → Prop
n : ℕ
hind : ∀ (m : ℕ), m < n → 8 ≤ m → from_three_five m
h : 8 ≤ n
htri : 11 ≤ n
⊢ from_three_five n
Tactic:
{
  sorry
}
State after:
case inr
P : ℕ → Prop
n : ℕ
hind : ∀ (m : ℕ), m < n → 8 ≤ m → from_three_five m
h : 8 ≤ n
htri : 11 ≤ n
⊢ from_three_five n

State before:
case inr
P : ℕ → Prop
n : ℕ
hind : ∀ (m : ℕ), m < n → 8 ≤ m → from_three_five m
h : 8 ≤ n
htri : 11 ≤ n
⊢ from_three_five n
Tactic:
{
  sorry
}
State after:
no goals

State before:
case inl
P : ℕ → Prop
n : ℕ
hind : ∀ (m : ℕ), m < n → 8 ≤ m → from_three_five m
h : 8 ≤ n
htri : n < 11
⊢ from_three_five n
Tactic:
sorry
State after:
no goals

State before:
case inr
P : ℕ → Prop
n : ℕ
hind : ∀ (m : ℕ), m < n → 8 ≤ m → from_three_five m
h : 8 ≤ n
htri : 11 ≤ n
⊢ from_three_five n
Tactic:
sorry
State after:
no goals