Nuprl Lemma : subtype_rel_partial
∀[A,B:Type]. partial(A) ⊆r partial(B) supposing A ⊆r B
Proof
Definitions occuring in Statement :
partial: partial(T),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
partial: partial(T),
quotient: x,y:A//B[x; y],
and: P ∧ Q,
so_lambda: λ2x y.t[x; y],
base-partial: base-partial(T),
so_apply: x[s1;s2],
all: ∀x:A. B[x],
guard: {T},
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
implies: P ⇒ Q,
cand: A c∧ B,
per-partial: per-partial(T;x;y),
uiff: uiff(P;Q)
Lemmas referenced :
partial_wf,
quotient-member-eq,
base-partial_wf,
per-partial_wf,
per-partial-equiv_rel,
subtype_rel_sets,
base_wf,
has-value_wf_base,
equal-wf-base,
not_wf,
is-exception_wf,
subtype_rel_wf,
equal_functionality_wrt_subtype_rel2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
sqequalHypSubstitution,
pointwiseFunctionalityForEquality,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
pertypeElimination,
productElimination,
setElimination,
rename,
independent_isectElimination,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
applyEquality,
because_Cache,
productEquality,
isectEquality,
setEquality,
lambdaFormation,
independent_pairFormation,
axiomEquality,
independent_functionElimination,
cumulativity,
isect_memberEquality,
universeEquality,
promote_hyp
Latex:
\mforall{}[A,B:Type]. partial(A) \msubseteq{}r partial(B) supposing A \msubseteq{}r B
Date html generated:
2016_05_14-AM-06_09_33
Last ObjectModification:
2015_12_26-AM-11_52_28
Theory : partial_1
Home
Index