Nuprl Lemma : name-morph-satisfies-0
∀[I:fset(ℕ)]. ∀[i:ℕ]. ((i=0) (i0)) = 1
Proof
Definitions occuring in Statement :
name-morph-satisfies: (psi f) = 1,
fl0: (x=0),
nc-0: (i0),
add-name: I+i,
fset: fset(T),
nat: ℕ,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
names: names(I),
subtype_rel: A ⊆r B,
uimplies: b supposing a,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
uiff: uiff(P;Q),
and: P ∧ Q,
nc-0: (i0),
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
empty-fset: {},
nil: [],
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],
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),
exists: ∃x:A. B[x],
squash: ↓T,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
bnot: ¬bb,
not: ¬A,
false: False,
or: P ∨ Q,
sq_type: SQType(T),
assert: ↑b,
nequal: a ≠ b ∈ T ,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
name-morph-satisfies: (psi f) = 1
Lemmas referenced :
name-morph-satisfies-fl0,
add-name_wf,
trivial-member-add-name1,
fset-member_wf,
nat_wf,
int-deq_wf,
strong-subtype-deq-subtype,
strong-subtype-set3,
le_wf,
istype-int,
strong-subtype-self,
nc-0_wf,
eq_int_wf,
eqtt_to_assert,
assert_of_eq_int,
dM0_wf,
eqff_to_assert,
assert_elim,
bnot_wf,
equal_wf,
squash_wf,
true_wf,
istype-universe,
bool_wf,
eq_int_eq_true,
subtype_rel_self,
iff_weakening_equal,
bfalse_wf,
bool_subtype_base,
set_subtype_base,
int_subtype_base,
btrue_neq_bfalse,
bool_cases_sqequal,
subtype_base_sq,
assert-bnot,
neg_assert_of_eq_int,
nat_properties,
full-omega-unsat,
intformnot_wf,
intformeq_wf,
itermVar_wf,
int_formula_prop_not_lemma,
istype-void,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
istype-nat,
fset_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
dependent_functionElimination,
dependent_set_memberEquality_alt,
universeIsType,
applyEquality,
intEquality,
independent_isectElimination,
because_Cache,
sqequalRule,
lambdaEquality_alt,
closedConclusion,
natural_numberEquality,
productElimination,
setElimination,
rename,
inhabitedIsType,
lambdaFormation_alt,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
dependent_pairFormation_alt,
equalityIsType4,
baseApply,
baseClosed,
imageElimination,
instantiate,
universeEquality,
imageMemberEquality,
independent_functionElimination,
independent_pairFormation,
productIsType,
applyLambdaEquality,
voidElimination,
promote_hyp,
cumulativity,
approximateComputation,
int_eqEquality,
isect_memberEquality_alt,
equalityIsType1,
axiomEquality,
isectIsTypeImplies
Latex:
\mforall{}[I:fset(\mBbbN{})]. \mforall{}[i:\mBbbN{}]. ((i=0) (i0)) = 1
Date html generated:
2019_11_04-PM-05_34_46
Last ObjectModification:
2018_11_08-AM-11_06_46
Theory : cubical!type!theory
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