Nuprl Lemma : free-append-0
∀[X:Type]. ∀[w:free-word(X)]. (w + 0 = w ∈ free-word(X))
Proof
Definitions occuring in Statement :
free-0: 0,
free-append: w + w',
free-word: free-word(X),
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
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,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
free-0: 0,
free-append: w + w',
quotient: x,y:A//B[x; y],
and: P ∧ Q,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
equiv_rel: EquivRel(T;x,y.E[x; y]),
refl: Refl(T;x,y.E[x; y])
Lemmas referenced :
list_wf,
word-equiv_wf,
word-equiv-equiv,
quotient-member-eq,
append_wf,
nil_wf,
append_back_nil,
equal-wf-base,
equal_wf,
squash_wf,
true_wf,
free-word_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
extract_by_obid,
isectElimination,
thin,
unionEquality,
cumulativity,
hypothesisEquality,
hypothesis,
promote_hyp,
lambdaFormation,
equalityTransitivity,
equalitySymmetry,
because_Cache,
independent_pairFormation,
sqequalRule,
lambdaEquality,
independent_isectElimination,
dependent_functionElimination,
independent_functionElimination,
pointwiseFunctionality,
pertypeElimination,
productElimination,
productEquality,
applyEquality,
imageElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
universeEquality,
isect_memberEquality,
axiomEquality
Latex:
\mforall{}[X:Type]. \mforall{}[w:free-word(X)]. (w + 0 = w)
Date html generated:
2020_05_20-AM-08_22_24
Last ObjectModification:
2017_07_28-AM-09_18_41
Theory : free!groups
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