Nuprl Lemma : norm_subset_p_wf
∀[g:GrpSig]. ∀[s:|g| ⟶ ℙ]. (norm_subset_p(g;s) ∈ ℙ)
Proof
Definitions occuring in Statement :
norm_subset_p: norm_subset_p(g;s),
grp_car: |g|,
grp_sig: GrpSig,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
norm_subset_p: norm_subset_p(g;s),
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
infix_ap: x f y,
so_apply: x[s]
Lemmas referenced :
all_wf,
grp_car_wf,
grp_op_wf,
grp_inv_wf,
grp_sig_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
functionEquality,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
cumulativity,
universeEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[g:GrpSig]. \mforall{}[s:|g| {}\mrightarrow{} \mBbbP{}]. (norm\_subset\_p(g;s) \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-00_08_53
Last ObjectModification:
2015_12_26-PM-11_45_39
Theory : groups_1
Home
Index