Nuprl Lemma : UallTest1
∀F:∀[T:Type]. (T ⟶ T). ∀S:Type. ∀s:S.  ((F s) = s ∈ S)
Proof
Definitions occuring in Statement : 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
apply: f a
, 
function: x:A ⟶ B[x]
, 
universe: Type
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
prop: ℙ
, 
uall: ∀[x:A]. B[x]
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
subtype_rel: A ⊆r B
, 
squash: ↓T
Lemmas referenced : 
set_wf, 
uall_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation, 
cut, 
hypothesis, 
hypothesisEquality, 
universeEquality, 
instantiate, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
sqequalRule, 
lambdaEquality, 
cumulativity, 
functionEquality, 
applyEquality, 
setEquality, 
equalityEquality, 
equalityTransitivity, 
equalitySymmetry, 
isectEquality, 
dependent_functionElimination, 
dependent_set_memberEquality, 
setElimination, 
rename, 
imageMemberEquality, 
baseClosed, 
introduction, 
imageElimination
Latex:
\mforall{}F:\mforall{}[T:Type].  (T  {}\mrightarrow{}  T).  \mforall{}S:Type.  \mforall{}s:S.    ((F  s)  =  s)
Date html generated:
2016_05_16-AM-09_05_03
Last ObjectModification:
2016_01_17-AM-09_41_27
Theory : C-semantics
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