Nuprl Lemma : trivial_nat1_fun
∀f:ℕ1 ⟶ ℕ1. (f = Id ∈ (ℕ1 ⟶ ℕ1))
Proof
Definitions occuring in Statement :
identity: Id,
int_seg: {i..j-},
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
identity: Id,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
prop: ℙ,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top
Lemmas referenced :
decidable__lt,
decidable__le,
int_formula_prop_wf,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformle_wf,
itermConstant_wf,
intformless_wf,
itermVar_wf,
intformeq_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__equal_int,
lelt_wf,
int_seg_properties,
int_seg_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
functionEquality,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
hypothesis,
functionExtensionality,
dependent_functionElimination,
hypothesisEquality,
sqequalRule,
applyEquality,
lambdaEquality,
setElimination,
rename,
setEquality,
intEquality,
productElimination,
equalityTransitivity,
equalitySymmetry,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
dependent_set_memberEquality,
because_Cache
Latex:
\mforall{}f:\mBbbN{}1 {}\mrightarrow{} \mBbbN{}1. (f = Id)
Date html generated:
2016_05_16-AM-07_32_08
Last ObjectModification:
2016_01_16-PM-10_06_08
Theory : perms_1
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