Nuprl Lemma : coded-code-pair
∀[a,b:ℕ]. (coded-pair(code-pair(a;b)) = <a, b> ∈ (ℕ × ℕ))
Proof
Definitions occuring in Statement :
code-pair: code-pair(a;b),
coded-pair: coded-pair(m),
nat: ℕ,
uall: ∀[x:A]. B[x],
pair: <a, b>,
product: x:A × B[x],
equal: s = t ∈ T
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],
code-pair: code-pair(a;b),
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
guard: {T},
uiff: uiff(P;Q),
sq_type: SQType(T),
cand: A c∧ B,
squash: ↓T,
le: A ≤ B,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
subtract: n - m
Lemmas referenced :
value-type-has-value,
nat_wf,
set-value-type,
le_wf,
int-value-type,
code-pair_wf,
tsqrt_wf,
triangular-num_wf,
nat_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
add_nat_wf,
add-is-int-iff,
intformeq_wf,
int_formula_prop_eq_lemma,
false_wf,
equal_wf,
subtract_wf,
subtype_base_sq,
set_subtype_base,
int_subtype_base,
tsqrt-unique,
decidable__equal_int,
less_than_wf,
squash_wf,
true_wf,
triangular-num-add1,
iff_weakening_equal,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
add-associates,
minus-one-mul,
add-swap,
minus-one-mul-top,
add-commutes,
add-mul-special,
zero-mul,
add-zero,
minus-add,
minus-minus,
zero-add
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
callbyvalueReduce,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
independent_isectElimination,
intEquality,
lambdaEquality,
natural_numberEquality,
hypothesisEquality,
dependent_set_memberEquality,
addEquality,
setElimination,
rename,
because_Cache,
dependent_functionElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
applyEquality,
lambdaFormation,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
pointwiseFunctionality,
promote_hyp,
baseApply,
closedConclusion,
baseClosed,
productElimination,
independent_functionElimination,
axiomEquality,
instantiate,
cumulativity,
imageElimination,
imageMemberEquality,
universeEquality,
independent_pairEquality,
minusEquality
Latex:
\mforall{}[a,b:\mBbbN{}]. (coded-pair(code-pair(a;b)) = <a, b>)
Date html generated:
2018_05_21-PM-07_54_42
Last ObjectModification:
2017_07_26-PM-05_32_15
Theory : general
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