Nuprl Lemma : f-subset-add-name1
∀I:fset(ℕ). ∀[J:fset(ℕ)]. ∀i:ℕ. (J ⊆ I ⇒ J ⊆ I+i)
Proof
Definitions occuring in Statement :
add-name: I+i,
f-subset: xs ⊆ ys,
fset: fset(T),
int-deq: IntDeq,
nat: ℕ,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
f-subset: xs ⊆ ys,
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
guard: {T},
or: P ∨ Q,
prop: ℙ,
nat: ℕ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
fset-member-add-name,
equal_wf,
fset-member_witness,
fset-member_wf,
nat_wf,
int-deq_wf,
f-subset_wf,
strong-subtype-deq-subtype,
strong-subtype-set3,
le_wf,
strong-subtype-self,
add-name_wf,
fset_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
productElimination,
independent_isectElimination,
sqequalRule,
hypothesis,
inrFormation,
isectElimination,
intEquality,
setElimination,
rename,
because_Cache,
independent_functionElimination,
applyEquality,
lambdaEquality,
natural_numberEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}I:fset(\mBbbN{}). \mforall{}[J:fset(\mBbbN{})]. \mforall{}i:\mBbbN{}. (J \msubseteq{} I {}\mRightarrow{} J \msubseteq{} I+i)
Date html generated:
2016_05_18-PM-00_00_11
Last ObjectModification:
2015_12_28-PM-03_06_29
Theory : cubical!type!theory
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