Nuprl Lemma : sg-inv_functionality
∀[sg:s-GroupStructure]. ∀[x1,x2:Point]. x1^-1 ≡ x2^-1 supposing x1 ≡ x2
Proof
Definitions occuring in Statement :
s-group-structure: s-GroupStructure,
sg-inv: x^-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,
all: ∀x:A. B[x],
false: False,
prop: ℙ,
subtype_rel: A ⊆r B
Lemmas referenced :
sg-inv-sep,
ss-sep_wf,
sg-inv_wf,
s-group-structure_subtype1,
ss-eq_wf,
ss-point_wf,
s-group-structure_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
lambdaFormation,
independent_functionElimination,
thin,
extract_by_obid,
dependent_functionElimination,
hypothesisEquality,
hypothesis,
voidElimination,
isectElimination,
applyEquality,
because_Cache,
sqequalRule,
lambdaEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[sg:s-GroupStructure]. \mforall{}[x1,x2:Point]. x1\^{}-1 \mequiv{} x2\^{}-1 supposing x1 \mequiv{} x2
Date html generated:
2017_10_02-PM-03_24_35
Last ObjectModification:
2017_06_23-AM-11_14_24
Theory : constructive!algebra
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