Nuprl Lemma : evalall-atom
∀[x:Atom]. (evalall(x) ~ x)
Proof
Definitions occuring in Statement : 
evalall: evalall(t)
, 
uall: ∀[x:A]. B[x]
, 
atom: Atom
, 
sqequal: s ~ t
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
uimplies: b supposing a
, 
evalall: evalall(t)
, 
has-value: (a)↓
, 
sq_type: SQType(T)
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
guard: {T}
, 
subtype_rel: A ⊆r B
, 
or: P ∨ Q
, 
not: ¬A
, 
false: False
, 
outl: outl(x)
, 
outr: outr(x)
Lemmas referenced : 
subtype_base_sq, 
atom_subtype_base, 
istype-atom, 
has-value-implies-dec-ispair, 
not-btrue-sqeq-bfalse, 
has-value-implies-dec-isinl, 
has-value-implies-dec-isinr
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
Error :isect_memberFormation_alt, 
introduction, 
cut, 
thin, 
instantiate, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
cumulativity, 
atomEquality, 
independent_isectElimination, 
hypothesis, 
sqequalRule, 
callbyvalueReduce, 
callbyvalueAtom, 
hypothesisEquality, 
dependent_functionElimination, 
equalityTransitivity, 
equalitySymmetry, 
independent_functionElimination, 
axiomSqEquality, 
baseApply, 
closedConclusion, 
baseClosed, 
applyEquality, 
unionElimination, 
isatomReduceTrue, 
because_Cache, 
voidElimination
Latex:
\mforall{}[x:Atom].  (evalall(x)  \msim{}  x)
Date html generated:
2019_06_20-AM-11_21_01
Last ObjectModification:
2018_10_16-PM-02_57_09
Theory : call!by!value_1
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