Nuprl Lemma : face-type-sq
𝔽 ~ <λI,alpha. Point(face_lattice(I)), λI,J,f,alpha,w. (w)<f>>
Proof
Definitions occuring in Statement :
face-type: 𝔽,
fl-morph: <f>,
face_lattice: face_lattice(I),
lattice-point: Point(l),
apply: f a,
lambda: λx.A[x],
pair: <a, b>,
sqequal: s ~ t
Definitions unfolded in proof :
face-type: 𝔽,
constant-cubical-type: (X),
I_cube: A(I),
functor-ob: ob(F),
pi1: fst(t),
face-presheaf: 𝔽,
lattice-point: Point(l),
record-select: r.x,
face_lattice: face_lattice(I),
face-lattice: face-lattice(T;eq),
free-dist-lattice-with-constraints: free-dist-lattice-with-constraints(T;eq;x.Cs[x]),
constrained-antichain-lattice: constrained-antichain-lattice(T;eq;P),
mk-bounded-distributive-lattice: mk-bounded-distributive-lattice,
mk-bounded-lattice: mk-bounded-lattice(T;m;j;z;o),
record-update: r[x := v],
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
bfalse: ff,
btrue: tt,
cube-set-restriction: f(s),
pi2: snd(t),
fl-morph: <f>,
fl-lift: fl-lift(T;eq;L;eqL;f0;f1),
face-lattice-property,
free-dist-lattice-with-constraints-property,
lattice-extend-wc: lattice-extend-wc(L;eq;eqL;f;ac),
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
Lemmas referenced :
face-lattice-property,
free-dist-lattice-with-constraints-property
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalTransitivity,
computationStep,
sqequalReflexivity
Latex:
\mBbbF{} \msim{} <\mlambda{}I,alpha. Point(face\_lattice(I)), \mlambda{}I,J,f,alpha,w. (w)<f>>
Date html generated:
2019_11_04-PM-05_37_07
Last ObjectModification:
2019_04_09-PM-03_09_59
Theory : cubical!type!theory
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