Nuprl Lemma : free-letter_wf
∀[X:Type]. ∀[x:X]. (free-letter(x) ∈ free-word(X))
Proof
Definitions occuring in Statement :
free-letter: free-letter(x),
free-word: free-word(X),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
free-word: free-word(X),
uall: ∀[x:A]. B[x],
member: t ∈ T,
free-letter: free-letter(x),
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a
Lemmas referenced :
cons_wf,
nil_wf,
subtype_quotient,
list_wf,
word-equiv_wf,
word-equiv-equiv
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
unionEquality,
cumulativity,
hypothesisEquality,
inlEquality,
hypothesis,
applyEquality,
lambdaEquality,
independent_isectElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[X:Type]. \mforall{}[x:X]. (free-letter(x) \mmember{} free-word(X))
Date html generated:
2020_05_20-AM-08_22_46
Last ObjectModification:
2017_01_15-PM-01_15_50
Theory : free!groups
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