Nuprl Lemma : s-group-axioms_wf
∀[sg:s-GroupStructure]. (s-group-axioms(sg) ∈ ℙ)
Proof
Definitions occuring in Statement :
s-group-axioms: s-group-axioms(sg),
s-group-structure: s-GroupStructure,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
s-group-axioms: s-group-axioms(sg),
prop: ℙ,
and: P ∧ Q,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
uall_wf,
ss-point_wf,
s-group-structure_subtype1,
ss-eq_wf,
sg-op_wf,
sg-id_wf,
sg-inv_wf,
s-group-structure_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
productEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
hypothesis,
lambdaEquality,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[sg:s-GroupStructure]. (s-group-axioms(sg) \mmember{} \mBbbP{})
Date html generated:
2017_10_02-PM-03_24_40
Last ObjectModification:
2017_06_23-AM-11_18_33
Theory : constructive!algebra
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