Nuprl Lemma : f-subset-add-name
∀I:fset(ℕ). ∀i:ℕ. I ⊆ I+i
Proof
Definitions occuring in Statement :
add-name: I+i,
f-subset: xs ⊆ ys,
fset: fset(T),
int-deq: IntDeq,
nat: ℕ,
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
f-subset: xs ⊆ ys,
uimplies: b supposing a,
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
guard: {T},
or: P ∨ Q,
prop: ℙ,
uall: ∀[x:A]. B[x],
nat: ℕ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q
Lemmas referenced :
fset-member-add-name,
equal_wf,
fset-member_witness,
int-deq_wf,
strong-subtype-deq-subtype,
nat_wf,
strong-subtype-set3,
le_wf,
strong-subtype-self,
add-name_wf,
fset-member_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,
applyEquality,
lambdaEquality,
natural_numberEquality,
independent_functionElimination
Latex:
\mforall{}I:fset(\mBbbN{}). \mforall{}i:\mBbbN{}. I \msubseteq{} I+i
Date html generated:
2016_05_18-PM-00_00_13
Last ObjectModification:
2015_12_28-PM-03_06_20
Theory : cubical!type!theory
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