Nuprl Lemma : free-word-inv_wf
∀[X:Type]. ∀[w:free-word(X)]. (free-word-inv(w) ∈ free-word(X))
Proof
Definitions occuring in Statement :
free-word-inv: free-word-inv(w),
free-word: free-word(X),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
free-word: free-word(X),
all: ∀x:A. B[x],
prop: ℙ,
implies: P ⇒ Q,
cand: A c∧ B,
free-word-inv: free-word-inv(w),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
guard: {T},
quotient: x,y:A//B[x; y],
and: P ∧ Q,
squash: ↓T,
true: True,
equiv_rel: EquivRel(T;x,y.E[x; y]),
refl: Refl(T;x,y.E[x; y]),
word-equiv: word-equiv(X;w1;w2),
exists: ∃x:A. B[x],
subtype_rel: A ⊆r B,
word-rel: word-rel(X;w1;w2),
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
so_lambda: λ2x.t[x],
so_apply: x[s],
label: ...$L... t,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
inverse-letters: a = -b,
or: P ∨ Q
Lemmas referenced :
word-equiv-equiv,
list_wf,
word-equiv_wf,
map_wf,
equal_wf,
reverse_wf,
quotient-member-eq,
equal-wf-base,
member_wf,
squash_wf,
true_wf,
free-word_wf,
transitive-reflexive-closure-map,
word-rel_wf,
transitive-reflexive-closure_wf,
subtype_rel_self,
inverse-letters_wf,
append_wf,
cons_wf,
nil_wf,
length_wf,
list_ind_cons_lemma,
list_ind_nil_lemma,
length-append,
exists_wf,
and_wf,
iff_weakening_equal,
free-word-inv-append,
subtype_rel_list,
top_wf,
append_assoc_sq,
reverse-cons,
reverse_nil_lemma,
map_cons_lemma,
map_nil_lemma,
decide_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
unionEquality,
hypothesis,
promote_hyp,
lambdaFormation,
equalityTransitivity,
equalitySymmetry,
because_Cache,
independent_pairFormation,
sqequalRule,
lambdaEquality,
unionElimination,
inrEquality,
inlEquality,
dependent_functionElimination,
independent_functionElimination,
independent_isectElimination,
pointwiseFunctionality,
pertypeElimination,
productElimination,
productEquality,
applyEquality,
imageElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
axiomEquality,
isect_memberEquality,
universeEquality,
dependent_pairFormation,
instantiate,
rename,
applyLambdaEquality,
voidElimination,
voidEquality,
dependent_set_memberEquality,
setElimination,
cumulativity,
hyp_replacement
Latex:
\mforall{}[X:Type]. \mforall{}[w:free-word(X)]. (free-word-inv(w) \mmember{} free-word(X))
Date html generated:
2019_10_31-AM-07_23_26
Last ObjectModification:
2018_08_21-PM-03_47_45
Theory : free!groups
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