Step
*
of Lemma
context-set-update-context4
No Annotations
∀X:?CubicalContext
(context-ok(X)
⇒ (∀[phi:Provisional''''(cttTerm(context-set(X)))]
∀X':?CubicalContext
((X' = update-context4{i:l}(X;phi) ∈ ?CubicalContext)
⇒ {allowed(phi)
⇒ type(allow(phi))=𝔽
⇒ (context-ok(X') ∧ (context-set(X') = context-set(X), term(allow(phi)) ∈ CubicalSet'''))})))
BY
{ (Intros THEN Unfold `guard` 0 THEN Auto) }
1
1. X : ?CubicalContext
2. context-ok(X)
3. [phi] : Provisional''''(cttTerm(context-set(X)))
4. X' : ?CubicalContext
5. X' = update-context4{i:l}(X;phi) ∈ ?CubicalContext
6. allowed(phi)
7. type(allow(phi))=𝔽
⊢ context-ok(X')
2
1. X : ?CubicalContext
2. context-ok(X)
3. phi : Provisional''''(cttTerm(context-set(X)))
4. X' : ?CubicalContext
5. X' = update-context4{i:l}(X;phi) ∈ ?CubicalContext
6. allowed(phi)
7. type(allow(phi))=𝔽
8. context-ok(X')
⊢ context-set(X') = context-set(X), term(allow(phi)) ∈ CubicalSet'''
Latex:
Latex:
No Annotations
\mforall{}X:?CubicalContext
(context-ok(X)
{}\mRightarrow{} (\mforall{}[phi:Provisional''''(cttTerm(context-set(X)))]
\mforall{}X':?CubicalContext
((X' = update-context4\{i:l\}(X;phi))
{}\mRightarrow{} \{allowed(phi)
{}\mRightarrow{} type(allow(phi))=\mBbbF{}
{}\mRightarrow{} (context-ok(X') \mwedge{} (context-set(X') = context-set(X), term(allow(phi))))\})))
By
Latex:
(Intros THEN Unfold `guard` 0 THEN Auto)
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