Nuprl Lemma : coded-pair_wf
∀[n:ℕ]. (coded-pair(n) ∈ ℕ × ℕ)
Proof
Definitions occuring in Statement :
coded-pair: coded-pair(m),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
product: x:A × B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
coded-pair: coded-pair(m),
has-value: (a)↓,
uimplies: b supposing a,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
and: P ∧ Q,
squash: ↓T,
prop: ℙ,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
ge: i ≥ j ,
all: ∀x:A. B[x],
le: A ≤ B,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
less_than: a < b,
uiff: uiff(P;Q)
Lemmas referenced :
false_wf,
int_term_value_add_lemma,
int_formula_prop_less_lemma,
itermAdd_wf,
intformless_wf,
add-is-int-iff,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_subtract_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermSubtract_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
nat_properties,
iff_weakening_equal,
triangular-num-add1,
true_wf,
squash_wf,
less_than_wf,
tsqrt-property,
triangular-num_wf,
subtract_wf,
tsqrt_wf,
int-value-type,
le_wf,
set-value-type,
nat_wf,
value-type-has-value
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
callbyvalueReduce,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
independent_isectElimination,
intEquality,
lambdaEquality,
natural_numberEquality,
hypothesisEquality,
because_Cache,
setElimination,
rename,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_pairFormation,
imageElimination,
imageMemberEquality,
baseClosed,
universeEquality,
independent_functionElimination,
promote_hyp,
independent_pairEquality,
dependent_set_memberEquality,
dependent_functionElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
pointwiseFunctionality,
baseApply,
closedConclusion
Latex:
\mforall{}[n:\mBbbN{}]. (coded-pair(n) \mmember{} \mBbbN{} \mtimes{} \mBbbN{})
Date html generated:
2019_06_20-PM-02_38_57
Last ObjectModification:
2019_06_12-PM-00_27_12
Theory : num_thy_1
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