Step
*
1
1
of Lemma
rel_plus-weak-TI
1. T : Type
2. R : T ⟶ T ⟶ ℙ
3. ∀Q:T ⟶ ℙ. weak-TI(T;x,y.R[x;y];x.Q[x])
4. Q : T ⟶ ℙ
5. ∀x:T. ((∀s:T. ((R+ x s)
⇒ Q[s]))
⇒ Q[x])
⊢ ∀x:T. Q[x]
BY
{ ((InstHyp [⌜λ2x.(∀s:T. ((R+ x s)
⇒ Q[s])) ∧ Q[x]⌝] 3⋅ THENA Auto) THEN D -1 THEN Auto) }
1
1. T : Type
2. R : T ⟶ T ⟶ ℙ
3. ∀Q:T ⟶ ℙ. weak-TI(T;x,y.R[x;y];x.Q[x])
4. Q : T ⟶ ℙ
5. ∀x:T. ((∀s:T. ((R+ x s)
⇒ Q[s]))
⇒ Q[x])
6. x : T
7. ∀s@0:T. (R[x;s@0]
⇒ ((∀s:T. ((R+ s@0 s)
⇒ Q[s])) ∧ Q[s@0]))
8. s : T
9. R+ x s
⊢ Q[s]
Latex:
Latex:
1. T : Type
2. R : T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}
3. \mforall{}Q:T {}\mrightarrow{} \mBbbP{}. weak-TI(T;x,y.R[x;y];x.Q[x])
4. Q : T {}\mrightarrow{} \mBbbP{}
5. \mforall{}x:T. ((\mforall{}s:T. ((R\msupplus{} x s) {}\mRightarrow{} Q[s])) {}\mRightarrow{} Q[x])
\mvdash{} \mforall{}x:T. Q[x]
By
Latex:
((InstHyp [\mkleeneopen{}\mlambda{}\msubtwo{}x.(\mforall{}s:T. ((R\msupplus{} x s) {}\mRightarrow{} Q[s])) \mwedge{} Q[x]\mkleeneclose{}] 3\mcdot{} THENA Auto) THEN D -1 THEN Auto)
Home
Index