Nuprl Lemma : nc-e-comp-nc-1
∀[I:fset(ℕ)]. ∀[i,j:{j:ℕ| ¬j ∈ I} ]. ((i1) = e(i;j) ⋅ (j1) ∈ I ⟶ I+i)
Proof
Definitions occuring in Statement :
nc-e: e(i;j),
nc-1: (i1),
add-name: I+i,
nh-comp: g ⋅ f,
names-hom: I ⟶ J,
fset-member: a ∈ s,
fset: fset(T),
int-deq: IntDeq,
nat: ℕ,
uall: ∀[x:A]. B[x],
not: ¬A,
set: {x:A| B[x]} ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
prop: ℙ,
uimplies: b supposing a,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
nc-1-as-nc-p,
fset_wf,
strong-subtype-self,
le_wf,
strong-subtype-set3,
strong-subtype-deq-subtype,
int-deq_wf,
fset-member_wf,
not_wf,
nat_wf,
dM1_wf,
nc-e-comp-nc-p
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
setEquality,
applyEquality,
because_Cache,
sqequalRule,
intEquality,
independent_isectElimination,
lambdaEquality,
natural_numberEquality,
setElimination,
rename,
equalitySymmetry
Latex:
\mforall{}[I:fset(\mBbbN{})]. \mforall{}[i,j:\{j:\mBbbN{}| \mneg{}j \mmember{} I\} ]. ((i1) = e(i;j) \mcdot{} (j1))
Date html generated:
2016_05_18-PM-00_03_29
Last ObjectModification:
2016_02_05-PM-02_15_28
Theory : cubical!type!theory
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