Nuprl Lemma : add-name-com
∀[I:fset(ℕ)]. ∀[i,j:ℕ]. (I+i+j = I+j+i ∈ fset(ℕ))
Proof
Definitions occuring in Statement :
add-name: I+i,
fset: fset(T),
nat: ℕ,
uall: ∀[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,
uimplies: b supposing a,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
uiff: uiff(P;Q),
and: P ∧ Q,
implies: P ⇒ Q,
prop: ℙ,
or: P ∨ Q,
guard: {T},
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
fset-extensionality,
int-deq_wf,
strong-subtype-deq-subtype,
nat_wf,
strong-subtype-set3,
le_wf,
strong-subtype-self,
add-name_wf,
fset-member_witness,
fset-member_wf,
or_wf,
equal_wf,
iff_transitivity,
iff_weakening_uiff,
fset-member-add-name
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
hypothesis,
applyEquality,
intEquality,
independent_isectElimination,
sqequalRule,
lambdaEquality,
natural_numberEquality,
hypothesisEquality,
productElimination,
independent_pairFormation,
independent_functionElimination,
independent_pairEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
axiomEquality,
setElimination,
rename,
unionElimination,
inrFormation,
inlFormation,
dependent_functionElimination,
lambdaFormation,
orFunctionality
Latex:
\mforall{}[I:fset(\mBbbN{})]. \mforall{}[i,j:\mBbbN{}]. (I+i+j = I+j+i)
Date html generated:
2016_05_18-PM-00_00_17
Last ObjectModification:
2015_12_28-PM-03_06_45
Theory : cubical!type!theory
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