Nuprl Lemma : assert-isdM1
∀[I:fset(ℕ)]. ∀[x:Point(dM(I))]. uiff(↑isdM1(x);x = 1 ∈ Point(dM(I)))
Proof
Definitions occuring in Statement :
isdM1: isdM1(x),
dM1: 1,
dM: dM(I),
fset: fset(T),
nat: ℕ,
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
equal: s = t ∈ T,
lattice-point: Point(l)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
isdM1: isdM1(x),
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
DeMorgan-algebra: DeMorganAlgebra,
so_lambda: λ2x.t[x],
prop: ℙ,
guard: {T},
so_apply: x[s],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
squash: ↓T
Lemmas referenced :
dM-point,
istype-void,
assert-deq-fset,
fset_wf,
names_wf,
deq-fset_wf,
union-deq_wf,
names-deq_wf,
fset-singleton_wf,
empty-fset_wf,
assert_witness,
isdM1_wf,
lattice-point_wf,
dM_wf,
subtype_rel_set,
DeMorgan-algebra-structure_wf,
lattice-structure_wf,
lattice-axioms_wf,
bounded-lattice-structure-subtype,
DeMorgan-algebra-structure-subtype,
subtype_rel_transitivity,
bounded-lattice-structure_wf,
bounded-lattice-axioms_wf,
equal_wf,
lattice-meet_wf,
lattice-join_wf,
DeMorgan-algebra-axioms_wf,
nat_wf,
iff_weakening_uiff,
assert_wf,
equal-wf-T-base,
istype-assert,
dM1_wf,
dM1-sq-singleton-empty,
fset-antichain_wf,
equal_functionality_wrt_subtype_rel2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
extract_by_obid,
isectElimination,
thin,
isect_memberEquality_alt,
voidElimination,
hypothesis,
setElimination,
rename,
hypothesisEquality,
unionEquality,
equalityTransitivity,
equalitySymmetry,
sqequalRule,
productElimination,
independent_pairEquality,
axiomEquality,
isectIsTypeImplies,
inhabitedIsType,
independent_functionElimination,
universeIsType,
applyEquality,
instantiate,
lambdaEquality_alt,
productEquality,
cumulativity,
because_Cache,
independent_isectElimination,
isectEquality,
baseClosed,
independent_pairFormation,
promote_hyp,
equalityIstype,
dependent_set_memberEquality_alt,
setEquality,
setIsType,
applyLambdaEquality,
imageMemberEquality,
imageElimination,
sqequalBase
Latex:
\mforall{}[I:fset(\mBbbN{})]. \mforall{}[x:Point(dM(I))]. uiff(\muparrow{}isdM1(x);x = 1)
Date html generated:
2020_05_20-PM-01_36_10
Last ObjectModification:
2019_12_10-PM-01_00_22
Theory : cubical!type!theory
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