Nuprl Lemma : sg-inv-of-op
∀[sg:s-Group]. ∀[x,y:Point]. (x y)^-1 ≡ (y^-1 x^-1)
Proof
Definitions occuring in Statement :
s-group: s-Group,
sg-op: (x y),
sg-inv: x^-1,
ss-eq: x ≡ y,
ss-point: Point,
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)
Lemmas referenced :
sg-inv-unique,
sg-op_wf,
sg-inv_wf,
ss-sep_wf,
s-group_subtype1,
ss-point_wf,
s-group_wf,
sg-id_wf,
ss-eq_functionality,
sg-assoc,
ss-eq_weakening,
sg-op_functionality,
ss-eq_inversion,
ss-eq_wf,
uiff_transitivity,
sg-op-inv,
ss-eq_transitivity,
sg-op-id
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_isectElimination,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
because_Cache,
applyEquality,
isect_memberEquality,
voidElimination,
independent_functionElimination,
productElimination
Latex:
\mforall{}[sg:s-Group]. \mforall{}[x,y:Point]. (x y)\^{}-1 \mequiv{} (y\^{}-1 x\^{}-1)
Date html generated:
2017_10_02-PM-03_25_04
Last ObjectModification:
2017_06_22-PM-06_30_23
Theory : constructive!algebra
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