Nuprl Lemma : nat-id-fun-example
∀n:ℕ. (∃m:ℕ [(m = n ∈ ℕ)])
Proof
Definitions occuring in Statement :
nat: ℕ,
all: ∀x:A. B[x],
sq_exists: ∃x:A [B[x]],
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
prop: ℙ,
decidable: Dec(P),
or: P ∨ Q,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
nat: ℕ,
sq_exists: ∃x:A [B[x]],
ge: i ≥ j ,
le: A ≤ B,
less_than': less_than'(a;b)
Lemmas referenced :
int_seg_properties,
full-omega-unsat,
intformand_wf,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
int_seg_wf,
decidable__equal_int,
subtract_wf,
subtype_base_sq,
set_subtype_base,
int_subtype_base,
intformnot_wf,
intformeq_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_subtract_lemma,
decidable__le,
decidable__lt,
le_wf,
less_than_wf,
subtype_rel_self,
guard_wf,
sq_exists_wf,
nat_wf,
equal-wf-base,
primrec-wf2,
all_wf,
nat_properties,
itermAdd_wf,
int_term_value_add_lemma,
istype-false,
set-value-type,
equal_wf,
int-value-type
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
thin,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
natural_numberEquality,
hypothesisEquality,
hypothesis,
setElimination,
rename,
productElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
lambdaEquality_alt,
int_eqEquality,
dependent_functionElimination,
isect_memberEquality_alt,
voidElimination,
sqequalRule,
independent_pairFormation,
universeIsType,
unionElimination,
applyEquality,
instantiate,
because_Cache,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
dependent_set_memberEquality_alt,
productIsType,
hypothesis_subsumption,
cumulativity,
intEquality,
functionIsType,
setIsType,
inhabitedIsType,
addEquality,
dependent_set_memberFormation_alt,
equalityIsType4,
baseClosed,
cutEval,
equalityIsType1,
baseApply,
closedConclusion
Latex:
\mforall{}n:\mBbbN{}. (\mexists{}m:\mBbbN{} [(m = n)])
Date html generated:
2019_10_16-AM-11_46_52
Last ObjectModification:
2018_10_10-PM-01_24_42
Theory : rationals
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