Nuprl Lemma : dM-lift-sq
∀[I',J',I,J,f:Top]. (dM-lift(I;J;f) ~ dM-lift(I';J';f))
Proof
Definitions occuring in Statement :
dM-lift: dM-lift(I;J;f),
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
dM-lift: dM-lift(I;J;f),
free-dma-lift: free-dma-lift(T;eq;dm;eq2;f),
free-DeMorgan-algebra-property,
free-dml-deq: free-dml-deq(T;eq),
dM: dM(I),
dma-neg: ¬(x),
union-deq: union-deq(A;B;a;b),
free-dist-lattice-property,
lattice-extend: lattice-extend(L;eq;eqL;f;ac),
free-DeMorgan-algebra: free-DeMorgan-algebra(T;eq),
lattice-fset-join: \/(s),
lattice-join: a ∨ b,
lattice-fset-meet: /\(s),
lattice-meet: a ∧ b,
free-DeMorgan-lattice: free-DeMorgan-lattice(T;eq),
mk-DeMorgan-algebra: mk-DeMorgan-algebra(L;n),
all: ∀x:A. B[x],
member: t ∈ T,
top: Top,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt,
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),
lattice-1: 1,
lattice-0: 0,
uall: ∀[x:A]. B[x],
dm-neg: ¬(x),
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,
record-select: r.x,
opposite-lattice: opposite-lattice(L),
record-update: r[x := v],
empty-fset: {},
nil: [],
it: ⋅,
so_lambda: λ2x y.t[x; y],
fset-singleton: {x},
cons: [a / b]
Lemmas referenced :
free-DeMorgan-algebra-property,
free-dist-lattice-property,
top_wf,
rec_select_update_lemma
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
because_Cache,
isect_memberFormation,
introduction,
sqequalAxiom,
isectElimination,
hypothesisEquality
Latex:
\mforall{}[I',J',I,J,f:Top]. (dM-lift(I;J;f) \msim{} dM-lift(I';J';f))
Date html generated:
2016_05_18-AM-11_57_58
Last ObjectModification:
2016_03_29-PM-00_35_24
Theory : cubical!type!theory
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