Nuprl Lemma : sg-inv-id
∀[sg:s-Group]. 1^-1 ≡ 1
Proof
Definitions occuring in Statement :
s-group: s-Group,
sg-inv: x^-1,
sg-id: 1,
ss-eq: x ≡ y,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ss-eq: x ≡ y,
not: ¬A,
implies: P ⇒ Q,
false: False,
subtype_rel: A ⊆r B,
prop: ℙ,
uimplies: b supposing a
Lemmas referenced :
ss-sep_wf,
s-group_subtype1,
sg-inv_wf,
sg-id_wf,
s-group_wf,
sg-op-id,
sg-inv-unique
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
lambdaEquality,
dependent_functionElimination,
thin,
hypothesisEquality,
voidElimination,
extract_by_obid,
isectElimination,
applyEquality,
hypothesis,
independent_isectElimination
Latex:
\mforall{}[sg:s-Group]. 1\^{}-1 \mequiv{} 1
Date html generated:
2017_10_02-PM-03_25_02
Last ObjectModification:
2017_06_22-PM-06_00_40
Theory : constructive!algebra
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