Nuprl Lemma : evalall-atom1
∀[x:Atom1]. (evalall(x) ~ x)
Proof
Definitions occuring in Statement :
evalall: evalall(t),
atom: Atom$n,
uall: ∀[x:A]. B[x],
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,
atom1_subtype_base,
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,
atomnEquality,
independent_isectElimination,
hypothesis,
sqequalRule,
callbyvalueReduce,
callbyvalueAtom1,
hypothesisEquality,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
axiomSqEquality,
Error :universeIsType,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
unionElimination,
isAtom1ReduceTrue,
because_Cache,
voidElimination
Latex:
\mforall{}[x:Atom1]. (evalall(x) \msim{} x)
Date html generated:
2019_06_20-AM-11_21_03
Last ObjectModification:
2018_10_15-AM-08_52_16
Theory : call!by!value_1
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