Nuprl Lemma : comb_for_itop_wf
λA,op,id,p,q,E,z. Π(op,id) p ≤ i < q. E[i] ∈ A:Type ⟶ op:(A ⟶ A ⟶ A) ⟶ id:A ⟶ p:ℤ ⟶ q:ℤ ⟶ E:({p..q-} ⟶ A) ⟶ (↓T\000Crue) ⟶ A
Proof
Definitions occuring in Statement :
itop: Π(op,id) lb ≤ i < ub. E[i],
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,
universe: Type
Definitions unfolded in proof :
member: t ∈ T,
squash: ↓T,
uall: ∀[x:A]. B[x],
prop: ℙ
Lemmas referenced :
itop_wf,
squash_wf,
true_wf,
int_seg_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
cut,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
functionEquality,
intEquality,
universeEquality
Latex:
\mlambda{}A,op,id,p,q,E,z. \mPi{}(op,id) p \mleq{} i < q. E[i] \mmember{} A:Type
{}\mrightarrow{} op:(A {}\mrightarrow{} A {}\mrightarrow{} A)
{}\mrightarrow{} id:A
{}\mrightarrow{} p:\mBbbZ{}
{}\mrightarrow{} q:\mBbbZ{}
{}\mrightarrow{} E:(\{p..q\msupminus{}\} {}\mrightarrow{} A)
{}\mrightarrow{} (\mdownarrow{}True)
{}\mrightarrow{} A
Date html generated:
2016_05_15-PM-00_14_34
Last ObjectModification:
2015_12_26-PM-11_40_57
Theory : groups_1
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