Nuprl Lemma : trivial-member-add-name2
∀I:fset(ℕ). ∀i:ℕ. ∀[j:ℕ]. i ∈ I+i+j
Proof
Definitions occuring in Statement :
add-name: I+i,
fset-member: a ∈ s,
fset: fset(T),
int-deq: IntDeq,
nat: ℕ,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
guard: {T},
or: P ∨ Q,
prop: ℙ,
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,
add-name_wf,
trivial-member-add-name1,
equal_wf,
fset-member_witness,
nat_wf,
int-deq_wf,
strong-subtype-deq-subtype,
strong-subtype-set3,
le_wf,
strong-subtype-self,
fset_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isectElimination,
hypothesisEquality,
hypothesis,
productElimination,
independent_isectElimination,
sqequalRule,
inrFormation,
intEquality,
setElimination,
rename,
applyEquality,
because_Cache,
lambdaEquality,
natural_numberEquality,
independent_functionElimination
Latex:
\mforall{}I:fset(\mBbbN{}). \mforall{}i:\mBbbN{}. \mforall{}[j:\mBbbN{}]. i \mmember{} I+i+j
Date html generated:
2016_05_18-PM-00_00_07
Last ObjectModification:
2015_12_28-PM-03_06_31
Theory : cubical!type!theory
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