Nuprl Lemma : free-group_wf
∀[X:Type]. (free-group(X) ∈ Group{i})
Proof
Definitions occuring in Statement :
free-group: free-group(X),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type,
grp: Group{i}
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
free-group: free-group(X),
member: t ∈ T,
assoc: Assoc(T;op),
infix_ap: x f y,
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
ident: Ident(T;op;id),
cand: A c∧ B,
inverse: Inverse(T;op;id;inv)
Lemmas referenced :
free-word_wf,
btrue_wf,
free-append_wf,
free-0_wf,
free-word-inv_wf,
equal_wf,
squash_wf,
true_wf,
free-append-assoc,
iff_weakening_equal,
free-append-0,
free-0-append,
free-word-inv-append2,
free-word-inv-append1,
mk_grp
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
universeEquality,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
lambdaEquality,
sqequalRule,
applyEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
because_Cache,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination,
independent_functionElimination,
isect_memberEquality,
axiomEquality,
independent_pairFormation,
independent_pairEquality
Latex:
\mforall{}[X:Type]. (free-group(X) \mmember{} Group\{i\})
Date html generated:
2020_05_20-AM-08_22_44
Last ObjectModification:
2017_07_28-AM-09_18_48
Theory : free!groups
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