Nuprl Lemma : fpf-empty-sub
∀[A:Type]. ∀[B,eq,g:Top]. ⊗ ⊆ g
Proof
Definitions occuring in Statement :
fpf-sub: f ⊆ g,
fpf-empty: ⊗,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
fpf-empty: ⊗,
fpf-sub: f ⊆ g,
all: ∀x:A. B[x],
member: t ∈ T,
top: Top,
fpf-dom: x ∈ dom(f),
pi1: fst(t),
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
implies: P ⇒ Q,
false: False,
prop: ℙ
Lemmas referenced :
fpf_ap_pair_lemma,
deq_member_nil_lemma,
false_wf,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
sqequalRule,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
lambdaFormation,
hypothesisEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[B,eq,g:Top]. \motimes{} \msubseteq{} g
Date html generated:
2018_05_21-PM-09_18_49
Last ObjectModification:
2018_02_09-AM-10_17_19
Theory : finite!partial!functions
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