Nuprl Lemma : FormSafe1-iff-FormSafe1''
∀C:Type. ∀f:Form(C). ∀vs:Atom List.  (FormSafe1(f) vs 
⇐⇒ FormSafe1''(f) vs)
Proof
Definitions occuring in Statement : 
FormSafe1'': FormSafe1''(f)
, 
FormSafe1: FormSafe1(f)
, 
Form: Form(C)
, 
list: T List
, 
all: ∀x:A. B[x]
, 
iff: P 
⇐⇒ Q
, 
apply: f a
, 
atom: Atom
, 
universe: Type
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
iff: P 
⇐⇒ Q
, 
and: P ∧ Q
, 
implies: P 
⇒ Q
, 
member: t ∈ T
, 
prop: ℙ
, 
uall: ∀[x:A]. B[x]
, 
rev_implies: P 
⇐ Q
, 
subtype_rel: A ⊆r B
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
Lemmas referenced : 
FormSafe1''_wf, 
list_wf, 
Form_wf, 
FormSafe1'-iff-FormSafe1'', 
FormSafe1'_wf, 
all_wf, 
iff_wf, 
FormSafe-iff-FormSafe1', 
FormSafe1_wf
Rules used in proof : 
cut, 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation, 
independent_pairFormation, 
hypothesis, 
applyEquality, 
introduction, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
cumulativity, 
hypothesisEquality, 
because_Cache, 
atomEquality, 
universeEquality, 
addLevel, 
allFunctionality, 
productElimination, 
impliesFunctionality, 
dependent_functionElimination, 
independent_functionElimination, 
lambdaEquality, 
sqequalRule, 
instantiate
Latex:
\mforall{}C:Type.  \mforall{}f:Form(C).  \mforall{}vs:Atom  List.    (FormSafe1(f)  vs  \mLeftarrow{}{}\mRightarrow{}  FormSafe1''(f)  vs)
Date html generated:
2018_05_21-PM-11_30_03
Last ObjectModification:
2017_10_12-PM-03_55_28
Theory : PZF
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