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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