Nuprl Lemma : comb_for_mon_itop_wf
λg,p,q,E,z. (Π p ≤ i < q. E[i]) ∈ g:IMonoid ⟶ p:ℤ ⟶ q:ℤ ⟶ E:({p..q-} ⟶ |g|) ⟶ (↓True) ⟶ |g|
Proof
Definitions occuring in Statement :
mon_itop: Π lb ≤ i < ub. E[i],
imon: IMonoid,
grp_car: |g|,
int_seg: {i..j-},
so_apply: x[s],
squash: ↓T,
true: True,
member: t ∈ T,
lambda: λx.A[x],
function: x:A ⟶ B[x],
int: ℤ
Definitions unfolded in proof :
member: t ∈ T,
squash: ↓T,
uall: ∀[x:A]. B[x],
prop: ℙ,
imon: IMonoid
Lemmas referenced :
mon_itop_wf,
squash_wf,
true_wf,
int_seg_wf,
grp_car_wf,
imon_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
cut,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
functionEquality,
setElimination,
rename,
intEquality
Latex:
\mlambda{}g,p,q,E,z. (\mPi{} p \mleq{} i < q. E[i]) \mmember{} g:IMonoid {}\mrightarrow{} p:\mBbbZ{} {}\mrightarrow{} q:\mBbbZ{} {}\mrightarrow{} E:(\{p..q\msupminus{}\} {}\mrightarrow{} |g|) {}\mrightarrow{} (\mdownarrow{}True) {}\mrightarrow{} |g|
Date html generated:
2016_05_15-PM-00_15_51
Last ObjectModification:
2015_12_26-PM-11_39_50
Theory : groups_1
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