Nuprl Lemma : word-equiv_wf
∀[X:Type]. ∀[w1,w2:(X + X) List]. (word-equiv(X;w1;w2) ∈ ℙ)
Proof
Definitions occuring in Statement :
word-equiv: word-equiv(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-equiv: word-equiv(X;w1;w2),
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
subtype_rel: A ⊆r B,
so_apply: x[s]
Lemmas referenced :
or_wf,
equal_wf,
list_wf,
exists_wf,
transitive-closure_wf,
word-rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
unionEquality,
cumulativity,
hypothesisEquality,
because_Cache,
hypothesis,
lambdaEquality,
productEquality,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[X:Type]. \mforall{}[w1,w2:(X + X) List]. (word-equiv(X;w1;w2) \mmember{} \mBbbP{})
Date html generated:
2020_05_20-AM-08_22_06
Last ObjectModification:
2017_01_13-PM-10_08_07
Theory : free!groups
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