Nuprl Lemma : mul-initial-seg_wf
∀[f:ℕ ⟶ ℕ]. (mul-initial-seg(f) ∈ ℕ ⟶ ℕ)
Proof
Definitions occuring in Statement :
mul-initial-seg: mul-initial-seg(f),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
mul-initial-seg: mul-initial-seg(f),
nat: ℕ,
prop: ℙ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x]
Lemmas referenced :
reduce_wf,
nat_wf,
mul_bounds_1a,
le_wf,
false_wf,
map_wf,
int_seg_wf,
subtype_rel_dep_function,
int_seg_subtype_nat,
subtype_rel_self,
upto_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
because_Cache,
dependent_set_memberEquality,
multiplyEquality,
setElimination,
rename,
hypothesisEquality,
natural_numberEquality,
independent_pairFormation,
lambdaFormation,
applyEquality,
independent_isectElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality
Latex:
\mforall{}[f:\mBbbN{} {}\mrightarrow{} \mBbbN{}]. (mul-initial-seg(f) \mmember{} \mBbbN{} {}\mrightarrow{} \mBbbN{})
Date html generated:
2016_05_15-PM-06_36_55
Last ObjectModification:
2015_12_27-AM-11_54_58
Theory : general
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