Nuprl Lemma : sq_stable__s-group-axioms
∀[sg:s-GroupStructure]. SqStable(s-group-axioms(sg))
Proof
Definitions occuring in Statement :
s-group-axioms: s-group-axioms(sg),
s-group-structure: s-GroupStructure,
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
s-group-axioms: s-group-axioms(sg),
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
and: P ∧ Q,
implies: P ⇒ Q,
sq_stable: SqStable(P),
ss-eq: x ≡ y,
not: ¬A,
false: False
Lemmas referenced :
sq_stable__and,
uall_wf,
ss-point_wf,
s-group-structure_subtype1,
ss-eq_wf,
sg-op_wf,
sg-id_wf,
sg-inv_wf,
sq_stable__uall,
sq_stable__ss-eq,
ss-sep_wf,
squash_wf,
s-group-axioms_wf,
s-group-structure_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
hypothesis,
sqequalRule,
lambdaEquality,
because_Cache,
isect_memberEquality,
productEquality,
independent_functionElimination,
dependent_functionElimination,
voidElimination,
lambdaFormation,
productElimination,
independent_pairEquality
Latex:
\mforall{}[sg:s-GroupStructure]. SqStable(s-group-axioms(sg))
Date html generated:
2017_10_02-PM-03_24_41
Last ObjectModification:
2017_06_23-AM-11_20_16
Theory : constructive!algebra
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