Nuprl Lemma : Q-R-glues-property
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[Qa,Rb:E ⟶ E ⟶ ℙ]. ∀[A,B:Type]. ∀[Ia:EClass(A)]. ∀[Ib:EClass(B)]. ∀[f:E(Ia) ⟶ B].
∀[g:E(Ib) ⟶ E].
g ∈ E(Ib) ⟶ E(Ia) supposing g glues Ia:Qa ──f⟶ Ib:Rb
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,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
prop: ℙ,
es-E-interface: E(X),
es-interface-predicate: {I},
top: Top,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
and: P ∧ Q,
Q-R-glues: g glues Ia:Qa ──f⟶ Ib:Rb,
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[Qa,Rb:E {}\mrightarrow{} E {}\mrightarrow{} \mBbbP{}]. \mforall{}[A,B:Type]. \mforall{}[Ia:EClass(A)]. \mforall{}[Ib:EClass(B)].
\mforall{}[f:E(Ia) {}\mrightarrow{} B]. \mforall{}[g:E(Ib) {}\mrightarrow{} E].
g \mmember{} E(Ib) {}\mrightarrow{} E(Ia) supposing g glues Ia:Qa {}{}f{}\mrightarrow{} Ib:Rb
Date html generated:
2016_05_17-AM-07_49_13
Last ObjectModification:
2015_12_28-PM-11_29_14
Theory : event-ordering
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