Nuprl Lemma : mon_itop_unroll_unit
∀[g:IMonoid]. ∀[i,j:ℤ]. ∀[E:{i..j-} ⟶ |g|]. ((Π i ≤ k < j. E[k]) = E[i] ∈ |g|) supposing (i + 1) = j ∈ ℤ
Proof
Definitions occuring in Statement :
mon_itop: Π lb ≤ i < ub. E[i],
imon: IMonoid,
grp_car: |g|,
int_seg: {i..j-},
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ⟶ B[x],
add: n + m,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
mon_itop: Π lb ≤ i < ub. E[i]
Lemmas referenced :
itop_unroll_unit
Rules used in proof :
cut,
lemma_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[i]) supposing (i + 1) = j
Date html generated:
2016_05_15-PM-00_16_01
Last ObjectModification:
2015_12_26-PM-11_40_01
Theory : groups_1
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