Nuprl Lemma : imonomial-less-transitive
∀[m1,m2,m3:iMonomial()]. (imonomial-less(m1;m3)) supposing (imonomial-less(m2;m3) and imonomial-less(m1;m2))
Proof
Definitions occuring in Statement :
imonomial-less: imonomial-less(m1;m2),
iMonomial: iMonomial(),
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
imonomial-less: imonomial-less(m1;m2),
and: P ∧ Q,
not: ¬A,
implies: P ⇒ Q,
false: False,
iMonomial: iMonomial(),
pi2: snd(t),
prop: ℙ,
uiff: uiff(P;Q),
imonomial-le: imonomial-le(m1;m2),
sq_type: SQType(T),
all: ∀x:A. B[x],
guard: {T},
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
equal_wf,
list_wf,
assert_witness,
imonomial-le_wf,
imonomial-less_wf,
iMonomial_wf,
eqtt_to_assert,
subtype_base_sq,
list_subtype_base,
int_subtype_base,
equal-wf-base,
set_subtype_base,
sorted_wf,
subtype_rel_self,
intlex-antisym,
intlex-transitive
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairFormation,
sqequalRule,
independent_pairEquality,
lambdaEquality,
dependent_functionElimination,
hypothesisEquality,
because_Cache,
extract_by_obid,
isectElimination,
intEquality,
hypothesis,
setElimination,
rename,
independent_functionElimination,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
voidElimination,
independent_isectElimination,
lambdaFormation,
promote_hyp,
instantiate,
cumulativity,
applyEquality
Latex:
\mforall{}[m1,m2,m3:iMonomial()].
(imonomial-less(m1;m3)) supposing (imonomial-less(m2;m3) and imonomial-less(m1;m2))
Date html generated:
2017_04_14-AM-08_57_39
Last ObjectModification:
2017_02_27-PM-03_40_48
Theory : omega
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