Nuprl Lemma : nat_well_founded
WellFnd{i}(ℕ;x,y.x < y)
Proof
Definitions occuring in Statement :
nat: ℕ,
wellfounded: WellFnd{i}(A;x,y.R[x; y]),
less_than: a < b
Definitions unfolded in proof :
wellfounded: WellFnd{i}(A;x,y.R[x; y]),
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
guard: {T},
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
nat: ℕ,
so_apply: x[s],
all: ∀x:A. B[x],
uimplies: b supposing a
Lemmas referenced :
all_wf,
nat_wf,
less_than_wf,
comp_nat_ind_a,
isect_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
sqequalRule,
lambdaEquality,
functionEquality,
setElimination,
rename,
hypothesisEquality,
applyEquality,
Error :functionIsType,
Error :universeIsType,
universeEquality,
instantiate,
independent_functionElimination,
dependent_functionElimination,
because_Cache,
independent_isectElimination
Latex:
WellFnd\{i\}(\mBbbN{};x,y.x < y)
Date html generated:
2019_06_20-AM-11_28_02
Last ObjectModification:
2018_09_26-AM-10_58_12
Theory : call!by!value_2
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