Nuprl Lemma : int_seg_well_founded_up
∀i:ℤ. ∀j:{i...}. WellFnd{i}({i..j-};x,y.x < y)
Proof
Definitions occuring in Statement :
int_upper: {i...},
int_seg: {i..j-},
wellfounded: WellFnd{i}(A;x,y.R[x; y]),
less_than: a < b,
all: ∀x:A. B[x],
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x y.t[x; y],
int_upper: {i...},
so_apply: x[s1;s2],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
implies: P ⇒ Q
Lemmas referenced :
int_upper_wf,
istype-int,
int_upper_well_founded,
inv_image_ind,
less_than_wf,
int_seg_wf,
int_seg_subtype_upper,
le_reflexive
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
Error :universeIsType,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
dependent_functionElimination,
sqequalRule,
Error :lambdaEquality_alt,
setElimination,
rename,
because_Cache,
Error :inhabitedIsType,
applyEquality,
independent_isectElimination,
independent_functionElimination
Latex:
\mforall{}i:\mBbbZ{}. \mforall{}j:\{i...\}. WellFnd\{i\}(\{i..j\msupminus{}\};x,y.x < y)
Date html generated:
2019_06_20-PM-01_15_21
Last ObjectModification:
2018_10_03-PM-10_11_28
Theory : int_2
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