Nuprl Lemma : fadd_wf
∀[n,m,k:ℕ]. ∀[f:ℕn ⟶ ℕm]. ∀[g:ℕn ⟶ ℕk + 1]. (fadd(f;g) ∈ ℕn ⟶ ℕm + k)
Proof
Definitions occuring in Statement :
fadd: fadd(f;g),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
add: n + m,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
fadd: fadd(f;g),
subtype_rel: A ⊆r B,
int_seg: {i..j-},
nat: ℕ,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
guard: {T},
lelt: i ≤ j < k,
ge: i ≥ j ,
all: ∀x:A. B[x],
prop: ℙ,
decidable: Dec(P),
or: P ∨ Q,
false: False,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top
Lemmas referenced :
add-member-int_seg1,
int_seg_wf,
int_seg_subtype,
subtract_wf,
int_seg_properties,
nat_properties,
decidable__le,
lelt_wf,
full-omega-unsat,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
int_formula_prop_wf,
intformless_wf,
itermAdd_wf,
int_formula_prop_less_lemma,
int_term_value_add_lemma,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
lambdaEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
hypothesisEquality,
hypothesis,
setElimination,
rename,
natural_numberEquality,
addEquality,
productElimination,
independent_isectElimination,
because_Cache,
independent_pairFormation,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
dependent_functionElimination,
functionExtensionality,
dependent_set_memberEquality,
unionElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
axiomEquality,
Error :functionIsType,
Error :universeIsType,
functionEquality,
Error :inhabitedIsType
Latex:
\mforall{}[n,m,k:\mBbbN{}]. \mforall{}[f:\mBbbN{}n {}\mrightarrow{} \mBbbN{}m]. \mforall{}[g:\mBbbN{}n {}\mrightarrow{} \mBbbN{}k + 1]. (fadd(f;g) \mmember{} \mBbbN{}n {}\mrightarrow{} \mBbbN{}m + k)
Date html generated:
2019_06_20-PM-02_28_58
Last ObjectModification:
2018_09_26-PM-05_50_50
Theory : num_thy_1
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