Nuprl Lemma : word-rel_wf
∀[X:Type]. ∀[w1,w2:(X + X) List]. (word-rel(X;w1;w2) ∈ ℙ)
Proof
Definitions occuring in Statement :
word-rel: word-rel(X;w1;w2),
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
union: left + right,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
word-rel: word-rel(X;w1;w2),
append: as @ bs,
all: ∀x:A. B[x],
so_lambda: so_lambda3,
top: Top,
so_apply: x[s1;s2;s3],
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
so_apply: x[s]
Lemmas referenced :
list_ind_cons_lemma,
list_ind_nil_lemma,
exists_wf,
list_wf,
inverse-letters_wf,
equal_wf,
append_wf,
cons_wf,
length_wf,
length-append
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isectElimination,
unionEquality,
cumulativity,
hypothesisEquality,
because_Cache,
lambdaEquality,
productEquality,
applyLambdaEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[X:Type]. \mforall{}[w1,w2:(X + X) List]. (word-rel(X;w1;w2) \mmember{} \mBbbP{})
Date html generated:
2020_05_20-AM-08_21_47
Last ObjectModification:
2017_07_28-AM-09_18_34
Theory : free!groups
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