Nuprl Lemma : interval-rev-1
∀[Gamma:j⊢]. (1-(1(𝕀)) = 0(𝕀) ∈ {Gamma ⊢ _:𝕀})
Proof
Definitions occuring in Statement :
interval-rev: 1-(r),
interval-1: 1(𝕀),
interval-0: 0(𝕀),
interval-type: 𝕀,
cubical-term: {X ⊢ _:A},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
interval-0: 0(𝕀),
dM0: 0,
lattice-0: 0,
record-select: r.x,
dM: dM(I),
free-DeMorgan-algebra: free-DeMorgan-algebra(T;eq),
mk-DeMorgan-algebra: mk-DeMorgan-algebra(L;n),
record-update: r[x := v],
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
bfalse: ff,
free-DeMorgan-lattice: free-DeMorgan-lattice(T;eq),
free-dist-lattice: free-dist-lattice(T; eq),
mk-bounded-distributive-lattice: mk-bounded-distributive-lattice,
mk-bounded-lattice: mk-bounded-lattice(T;m;j;z;o),
btrue: tt,
empty-fset: {},
nil: [],
it: ⋅,
interval-rev: 1-(r),
dma-neg: ¬(x),
dm-neg: ¬(x),
lattice-extend: lattice-extend(L;eq;eqL;f;ac),
lattice-fset-join: \/(s),
reduce: reduce(f;k;as),
list_ind: list_ind,
fset-image: f"(s),
f-union: f-union(domeq;rngeq;s;x.g[x]),
list_accum: list_accum,
cubical-term-at: u(a),
interval-1: 1(𝕀),
dM1: 1,
lattice-1: 1,
fset-singleton: {x},
cons: [a / b],
fset-union: x ⋃ y,
l-union: as ⋃ bs,
insert: insert(a;L),
eval_list: eval_list(t),
deq-member: x ∈b L,
lattice-join: a ∨ b,
opposite-lattice: opposite-lattice(L),
so_lambda: λ2x y.t[x; y],
lattice-meet: a ∧ b,
fset-ac-glb: fset-ac-glb(eq;ac1;ac2),
fset-minimals: fset-minimals(x,y.less[x; y]; s),
fset-filter: {x ∈ s | P[x]},
filter: filter(P;l),
lattice-fset-meet: /\(s),
member: t ∈ T,
subtype_rel: A ⊆r B,
cubical-term: {X ⊢ _:A},
uimplies: b supposing a
Lemmas referenced :
interval-rev_wf,
interval-1_wf,
I_cube_wf,
fset_wf,
nat_wf,
cubical-term-equal,
interval-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
functionExtensionality,
sqequalRule,
hypothesis,
applyEquality,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality_alt,
setElimination,
rename,
inhabitedIsType,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
universeIsType,
instantiate
Latex:
\mforall{}[Gamma:j\mvdash{}]. (1-(1(\mBbbI{})) = 0(\mBbbI{}))
Date html generated:
2020_05_20-PM-02_37_09
Last ObjectModification:
2020_04_04-AM-10_10_18
Theory : cubical!type!theory
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