Nuprl Lemma : sg-inv-unique
∀[sg:s-Group]. ∀[x,y:Point]. x^-1 ≡ y supposing (x y) ≡ 1
Proof
Definitions occuring in Statement :
s-group: s-Group,
sg-op: (x y),
sg-inv: x^-1,
sg-id: 1,
ss-eq: x ≡ y,
ss-point: Point,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
ss-eq: x ≡ y,
not: ¬A,
implies: P ⇒ Q,
false: False,
subtype_rel: A ⊆r B,
prop: ℙ,
all: ∀x:A. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q),
guard: {T}
Lemmas referenced :
ss-sep_wf,
s-group_subtype1,
sg-inv_wf,
ss-eq_wf,
sg-op_wf,
sg-id_wf,
ss-point_wf,
s-group_wf,
ss-eq_weakening,
ss-eq_functionality,
sg-op_functionality,
sg-assoc,
ss-eq_inversion,
uiff_transitivity,
sg-inv-op,
sg-op-id,
sg-id-op
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
lambdaEquality,
dependent_functionElimination,
thin,
hypothesisEquality,
because_Cache,
extract_by_obid,
isectElimination,
applyEquality,
hypothesis,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
voidElimination,
independent_functionElimination,
independent_isectElimination,
productElimination
Latex:
\mforall{}[sg:s-Group]. \mforall{}[x,y:Point]. x\^{}-1 \mequiv{} y supposing (x y) \mequiv{} 1
Date html generated:
2017_10_02-PM-03_24_57
Last ObjectModification:
2017_06_22-PM-05_59_04
Theory : constructive!algebra
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