Nuprl Lemma : Q-R-glues_functionality
∀[Info:Type]
∀es:EO+(Info)
∀[R:E ⟶ E ⟶ ℙ]. ∀[A,B:Type].
∀Ia:EClass(A). ∀Ib:EClass(B). ∀f:E(Ia) ⟶ B.
∀[Q1,Q2:E ⟶ E ⟶ ℙ]. ∀g:E(Ib) ⟶ E. (Q1 ⇐⇒ Q2 ⇒ (g glues Ia:Q1 ──f⟶ Ib:R ⇐⇒ g glues Ia:Q2 ──f⟶ Ib:R))
Proof
Definitions occuring in Statement :
Q-R-glues: g glues Ia:Qa ──f⟶ Ib:Rb,
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
rel_equivalent: R1 ⇐⇒ R2,
uall: ∀[x:A]. B[x],
prop: ℙ,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
es-E-interface: E(X),
so_apply: x[s],
so_lambda: λ2x.t[x],
top: Top,
uimplies: b supposing a,
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
rev_implies: P ⇐ Q,
prop: ℙ,
member: t ∈ T,
cand: A c∧ B,
Q-R-glues: g glues Ia:Qa ──f⟶ Ib:Rb,
and: P ∧ Q,
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
exists: ∃x:A. B[x],
es-interface-predicate: {I},
list_ind: list_ind,
length: ||as||,
bag-size: #(bs),
eq_int: (i =z j),
in-eclass: e ∈b X,
ifthenelse: if b then t else f fi ,
assert: ↑b,
predicate_rev_implies: P1 ⇐ P2,
rel_rev_implies: R1 ⇐ R2,
label: ...$L... t,
guard: {T},
rel_equivalent: R1 ⇐⇒ R2
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info)
\mforall{}[R:E {}\mrightarrow{} E {}\mrightarrow{} \mBbbP{}]. \mforall{}[A,B:Type].
\mforall{}Ia:EClass(A). \mforall{}Ib:EClass(B). \mforall{}f:E(Ia) {}\mrightarrow{} B.
\mforall{}[Q1,Q2:E {}\mrightarrow{} E {}\mrightarrow{} \mBbbP{}].
\mforall{}g:E(Ib) {}\mrightarrow{} E. (Q1 \mLeftarrow{}{}\mRightarrow{} Q2 {}\mRightarrow{} (g glues Ia:Q1 {}{}f{}\mrightarrow{} Ib:R \mLeftarrow{}{}\mRightarrow{} g glues Ia:Q2 {}{}f{}\mrightarrow{} Ib:R))
Date html generated:
2016_05_17-AM-07_49_40
Last ObjectModification:
2015_12_28-PM-11_53_19
Theory : event-ordering
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