Nuprl Lemma : sg-op-inv
∀[sg:s-Group]. ∀[x:Point]. (x x^-1) ≡ 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,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
s-group: s-Group,
ss-eq: x ≡ y,
not: ¬A,
implies: P ⇒ Q,
false: False,
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_stable: SqStable(P),
squash: ↓T,
s-group-axioms: s-group-axioms(sg),
and: P ∧ Q
Lemmas referenced :
ss-sep_wf,
s-group-structure_subtype1,
s-group_subtype1,
subtype_rel_transitivity,
s-group_wf,
s-group-structure_wf,
separation-space_wf,
sg-op_wf,
sg-inv_wf,
sg-id_wf,
ss-point_wf,
ss-eq_wf,
squash_wf,
sq_stable__uall,
sq_stable__ss-eq
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
sqequalRule,
isect_memberEquality,
isectElimination,
hypothesisEquality,
lambdaEquality,
dependent_functionElimination,
voidElimination,
extract_by_obid,
applyEquality,
hypothesis,
instantiate,
independent_isectElimination,
because_Cache,
independent_functionElimination,
imageMemberEquality,
baseClosed,
imageElimination,
productElimination
Latex:
\mforall{}[sg:s-Group]. \mforall{}[x:Point]. (x x\^{}-1) \mequiv{} 1
Date html generated:
2017_10_02-PM-03_24_51
Last ObjectModification:
2017_06_23-AM-11_23_12
Theory : constructive!algebra
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