Nuprl Lemma : mon_itop_unroll_empty
∀[g:IMonoid]. ∀[i,j:ℤ]. ∀[E:{i..j-} ⟶ |g|]. ((Π i ≤ k < j. E[k]) = e ∈ |g|) supposing j ≤ i
Proof
Definitions occuring in Statement :
mon_itop: Π lb ≤ i < ub. E[i],
imon: IMonoid,
grp_id: e,
grp_car: |g|,
int_seg: {i..j-},
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
le: A ≤ B,
function: x:A ⟶ B[x],
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
mon_itop: Π lb ≤ i < ub. E[i]
Lemmas referenced :
itop_unroll_empty
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
hypothesis
Latex:
\mforall{}[g:IMonoid]. \mforall{}[i,j:\mBbbZ{}]. \mforall{}[E:\{i..j\msupminus{}\} {}\mrightarrow{} |g|]. ((\mPi{} i \mleq{} k < j. E[k]) = e) supposing j \mleq{} i
Date html generated:
2019_10_15-AM-10_32_58
Last ObjectModification:
2019_08_13-PM-05_08_41
Theory : groups_1
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