Nuprl Lemma : fpf-compatible-singles-trivial
∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[B:Top]. ∀[x,y:A]. ∀[v,u:Top].  x : v || y : u supposing ¬(x = y ∈ A)
Proof
Definitions occuring in Statement : 
fpf-single: x : v
, 
fpf-compatible: f || g
, 
deq: EqDecider(T)
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
top: Top
, 
so_apply: x[s]
, 
not: ¬A
, 
universe: Type
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
fpf-compatible: f || g
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
not: ¬A
, 
fpf-single: x : v
, 
fpf-dom: x ∈ dom(f)
, 
pi1: fst(t)
, 
member: t ∈ T
, 
top: Top
, 
false: False
, 
prop: ℙ
, 
and: P ∧ Q
, 
uall: ∀[x:A]. B[x]
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
or: P ∨ Q
, 
uimplies: b supposing a
, 
eqof: eqof(d)
, 
iff: P 
⇐⇒ Q
, 
uiff: uiff(P;Q)
, 
assert: ↑b
, 
ifthenelse: if b then t else f fi 
, 
bfalse: ff
, 
rev_implies: P 
⇐ Q
Lemmas referenced : 
deq_member_cons_lemma, 
deq_member_nil_lemma, 
assert_wf, 
fpf-dom_wf, 
fpf-single_wf, 
top_wf, 
bor_wf, 
eqof_wf, 
bfalse_wf, 
or_wf, 
equal_wf, 
false_wf, 
not_wf, 
deq_wf, 
iff_transitivity, 
iff_weakening_uiff, 
assert_of_bor, 
safe-assert-deq
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation, 
sqequalHypSubstitution, 
independent_functionElimination, 
thin, 
sqequalRule, 
cut, 
introduction, 
extract_by_obid, 
dependent_functionElimination, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
hypothesis, 
productEquality, 
isectElimination, 
cumulativity, 
hypothesisEquality, 
instantiate, 
lambdaEquality, 
because_Cache, 
applyEquality, 
productElimination, 
unionElimination, 
equalityTransitivity, 
equalitySymmetry, 
universeEquality, 
isect_memberFormation, 
axiomEquality, 
addLevel, 
independent_pairFormation, 
orFunctionality, 
independent_isectElimination, 
levelHypothesis, 
promote_hyp, 
andLevelFunctionality
Latex:
\mforall{}[A:Type].  \mforall{}[eq:EqDecider(A)].  \mforall{}[B:Top].  \mforall{}[x,y:A].  \mforall{}[v,u:Top].    x  :  v  ||  y  :  u  supposing  \mneg{}(x  =  y)
Date html generated:
2018_05_21-PM-09_28_57
Last ObjectModification:
2018_02_09-AM-10_24_04
Theory : finite!partial!functions
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