Nuprl Lemma : fps-add-grp_wf
∀[X:Type]. ∀[eq:EqDecider(X)]. ∀[r:CRng]. (fps-add-grp(r) ∈ AbGrp) supposing valueall-type(X)
Proof
Definitions occuring in Statement :
fps-add-grp: fps-add-grp(r),
deq: EqDecider(T),
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type,
crng: CRng,
abgrp: AbGrp
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
fps-add-grp: fps-add-grp(r),
subtype_rel: A ⊆r B,
crng: CRng
Lemmas referenced :
add_grp_of_rng_wf_b,
fps-rng_wf,
crng_wf,
deq_wf,
valueall-type_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
applyEquality,
lambdaEquality,
setElimination,
rename,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[X:Type]. \mforall{}[eq:EqDecider(X)]. \mforall{}[r:CRng]. (fps-add-grp(r) \mmember{} AbGrp) supposing valueall-type(X)
Date html generated:
2016_05_15-PM-09_48_12
Last ObjectModification:
2015_12_27-PM-04_40_44
Theory : power!series
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