Nuprl Lemma : free-append_wf
∀[X:Type]. ∀[w,w':free-word(X)]. (w + w' ∈ free-word(X))
Proof
Definitions occuring in Statement :
free-append: w + 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,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
cand: A c∧ B,
quotient: x,y:A//B[x; y],
and: P ∧ Q,
squash: ↓T,
true: True,
guard: {T},
equiv_rel: EquivRel(T;x,y.E[x; y]),
refl: Refl(T;x,y.E[x; y]),
subtype_rel: A ⊆r B,
free-append: w + w',
word-equiv: word-equiv(X;w1;w2),
exists: ∃x:A. B[x],
infix_ap: x f y
Lemmas referenced :
free-word_wf,
list_wf,
word-equiv_wf,
quotient_wf,
word-equiv-equiv,
equal-wf-base,
member_wf,
squash_wf,
true_wf,
equal_wf,
quotient-member-eq,
append_wf,
transitive-reflexive-closure_wf,
word-rel_wf,
transitive-reflexive-closure-map,
word-rel-append1,
word-rel-append2,
transitive-reflexive-closure_transitivity
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
extract_by_obid,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
isect_memberEquality,
because_Cache,
universeEquality,
unionEquality,
promote_hyp,
lambdaFormation,
lambdaEquality,
dependent_functionElimination,
independent_isectElimination,
independent_pairFormation,
pointwiseFunctionality,
pertypeElimination,
productElimination,
independent_functionElimination,
productEquality,
applyEquality,
imageElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
dependent_pairFormation
Latex:
\mforall{}[X:Type]. \mforall{}[w,w':free-word(X)]. (w + w' \mmember{} free-word(X))
Date html generated:
2020_05_20-AM-08_22_19
Last ObjectModification:
2017_07_28-AM-09_18_40
Theory : free!groups
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