Nuprl Lemma : eqv_mod_subset_wf
∀[g:GrpSig]. ∀[s:|g| ⟶ ℙ]. ∀[a,b:|g|]. (a ≡ b (mod s in g) ∈ ℙ)
Proof
Definitions occuring in Statement :
eqv_mod_subset: a ≡ b (mod s in g),
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 :
eqv_mod_subset: a ≡ b (mod s in g),
uall: ∀[x:A]. B[x],
member: t ∈ T,
infix_ap: x f y,
prop: ℙ
Lemmas referenced :
grp_op_wf,
grp_inv_wf,
grp_car_wf,
grp_sig_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
applyEquality,
hypothesisEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
functionEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[g:GrpSig]. \mforall{}[s:|g| {}\mrightarrow{} \mBbbP{}]. \mforall{}[a,b:|g|]. (a \mequiv{} b (mod s in g) \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-00_09_03
Last ObjectModification:
2015_12_26-PM-11_45_32
Theory : groups_1
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