Nuprl Lemma : not-imonomial-le
∀a,b:iMonomial(). ((¬↑imonomial-le(a;b)) ⇒ imonomial-less(b;a))
Proof
Definitions occuring in Statement :
imonomial-less: imonomial-less(m1;m2),
imonomial-le: imonomial-le(m1;m2),
iMonomial: iMonomial(),
assert: ↑b,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
iMonomial: iMonomial(),
imonomial-le: imonomial-le(m1;m2),
pi2: snd(t),
imonomial-less: imonomial-less(m1;m2),
and: P ∧ Q,
cand: A c∧ B,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
not: ¬A,
uimplies: b supposing a,
sq_type: SQType(T),
guard: {T},
false: False,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
squash: ↓T,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
or: P ∨ Q
Lemmas referenced :
not_wf,
assert_wf,
imonomial-le_wf,
iMonomial_wf,
subtype_base_sq,
list_wf,
list_subtype_base,
int_subtype_base,
equal-wf-base,
set_subtype_base,
sorted_wf,
subtype_rel_self,
eqtt_to_assert,
intlex_wf,
equal_wf,
squash_wf,
true_wf,
bool_wf,
intlex-reflexive,
btrue_wf,
iff_weakening_equal,
intlex-total
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
cut,
independent_pairFormation,
hypothesis,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
independent_functionElimination,
instantiate,
cumulativity,
intEquality,
independent_isectElimination,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
voidElimination,
because_Cache,
applyEquality,
lambdaEquality,
setElimination,
rename,
imageElimination,
universeEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
unionElimination
Latex:
\mforall{}a,b:iMonomial(). ((\mneg{}\muparrow{}imonomial-le(a;b)) {}\mRightarrow{} imonomial-less(b;a))
Date html generated:
2017_04_14-AM-08_57_43
Last ObjectModification:
2017_02_27-PM-03_40_51
Theory : omega
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