Nuprl Lemma : mon_itop_wf
∀[g:IMonoid]. ∀[p,q:ℤ]. ∀[E:{p..q-} ⟶ |g|]. (Π p ≤ i < q. E[i] ∈ |g|)
Proof
Definitions occuring in Statement :
mon_itop: Π lb ≤ i < ub. E[i],
imon: IMonoid,
grp_car: |g|,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
int: ℤ
Definitions unfolded in proof :
mon_itop: Π lb ≤ i < ub. E[i],
uall: ∀[x:A]. B[x],
member: t ∈ T,
imon: IMonoid,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
itop_wf,
grp_car_wf,
grp_op_wf,
grp_id_wf,
int_seg_wf,
imon_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
lambdaEquality,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
isect_memberEquality,
because_Cache,
intEquality
Latex:
\mforall{}[g:IMonoid]. \mforall{}[p,q:\mBbbZ{}]. \mforall{}[E:\{p..q\msupminus{}\} {}\mrightarrow{} |g|]. (\mPi{} p \mleq{} i < q. E[i] \mmember{} |g|)
Date html generated:
2016_05_15-PM-00_15_47
Last ObjectModification:
2015_12_26-PM-11_40_09
Theory : groups_1
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